pacman::p_load(tmap, sf, sp,
performance, reshape2,
ggpubr, DT, stplanr, tidyverse)Hands-on Exercise 11
Hands-On Exercise
R
sf
GWmodel
SpatialML
Spatial Interaction Models
Calibrating Spatial Interaction Models with R
1.0 What is Spatial Interaction Modelling?
Spatial interaction modelling (or gravity models) is one of the most widely used analytical tools in studying interactions between social and economic agents observed in geographical space (Patuelli & Arbia, 2016). Spatial Interaction Models (SIMs) are mathematical models for estimating flows between spatial entities developed by Alan Wilson in the late 1960s and early 1970, with considerable uptake and refinement for transport modelling since then Boyce and Williams (2015). Spatial interaction models, in general terms, describe and explain flow or movement between places, based on (1) their spatial separation; (2) their complementarity; and (3) other intervening opportunities or spatial structural elements serve to augment or diminish the expected flow (O’Kelly, 2009).
There are four main types of traditional SIMs (Wilson 1971):
Unconstrained
Production-constrained
Attraction-constrained
Doubly-constrained
Ordinary least square (OLS), log-normal, Poisson and negative binomial (NB) regression methods have been used extensively to calibrate OD flow models by processing flow data as different types of dependent variables. In this execrise, we will explore how to calibrate SIM by using the four regression methods in R environment.
2.0 Importing Packages
Firstly, we will install and import necessary R-packages for this modelling exercise. The R packages needed for this exercise are as follows:
tmapwhich provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.sffor importing, managing and processing vector-based geospatial data in R.spfor handling spatial objectsperformancefor model comparison and calculating evaluation metricsreshape2for reshaping dataframes between ‘wide’ format with repeated measurements in separate columns of the same record and ‘long’ format with the repeated measurements in separate records.ggpubrfor creating publication-ready plotstidyversefor wrangling attribute data in Rstplanr provides functions for solving common problems in transport planning and modelling such as downloading and cleaning transport datasets; creating geographic “desire lines” from origin-destination (OD) data; route assignment, locally and interfaces to routing services such as CycleStreets.net; calculation of route segment attributes such as bearing and aggregate flow; and ‘travel watershed’ analysis.
DT provides an R interface to the JavaScript library DataTables. R data objects (matrices or data frames) can be displayed as tables on HTML pages, and DataTables provides filtering, pagination, sorting, and many other features in the tables.
3.0 Importing Datasets to R Environment
In this exercise, the following datasets will be used:
Passenger Volume by Origin Destination Bus Stops data set downloaded from LTA DataMall
BusStop: This data provides the location of bus stop as at last quarter of 2022.
MPSZ-2019: This data provides the sub-zone boundary of URA Master Plan 2019.
odbus <- read_csv("../data/aspatial/origin_destination_bus_202210.csv")Rows: 5122925 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (3): YEAR_MONTH, DAY_TYPE, PT_TYPE
dbl (4): TIME_PER_HOUR, ORIGIN_PT_CODE, DESTINATION_PT_CODE, TOTAL_TRIPS
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.busstop <- st_read(dsn = "../data/geospatial",
layer = "BusStop") %>%
st_transform(crs = 3414)Reading layer `BusStop' from data source
`/Users/khantminnaing/IS415-GAA/data/geospatial' using driver `ESRI Shapefile'
Simple feature collection with 5159 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21mpsz <- st_read(dsn = "../data/geospatial",
layer = "MPSZ-2019") %>%
st_transform(crs = 3414)Reading layer `MPSZ-2019' from data source
`/Users/khantminnaing/IS415-GAA/data/geospatial' using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS: WGS 844.0 Data Preparation & Wrangling
4.1 Aspatial Data Wrangling
Let’s have a look at the newly created odbus tibble data frame by using glimpse() function.
glimpse(odbus)Rows: 5,122,925
Columns: 7
$ YEAR_MONTH <chr> "2022-10", "2022-10", "2022-10", "2022-10", "2022-…
$ DAY_TYPE <chr> "WEEKDAY", "WEEKENDS/HOLIDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR <dbl> 10, 10, 7, 11, 16, 16, 20, 7, 7, 11, 11, 8, 11, 11…
$ PT_TYPE <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE <dbl> 65239, 65239, 23519, 52509, 54349, 54349, 43371, 8…
$ DESTINATION_PT_CODE <dbl> 65159, 65159, 23311, 42041, 53241, 53241, 14139, 9…
$ TOTAL_TRIPS <dbl> 2, 1, 2, 1, 1, 4, 1, 3, 1, 5, 2, 5, 15, 40, 1, 1, …A quick check of odbus tibble data frame shows that the values in OROGIN_PT_CODE and DESTINATON_PT_CODE are in numeric data type. Hence, the code chunk below is used to convert these data values into character data type.
odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE) Next, for the purpose of this exercise, we will extract commuting flows on weekday and between 6 and 9 o’clock.
odbus6_9 <- odbus %>%
filter(DAY_TYPE == "WEEKDAY") %>%
filter(TIME_PER_HOUR >= 6 &
TIME_PER_HOUR <= 9) %>%
group_by(ORIGIN_PT_CODE,
DESTINATION_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))`summarise()` has grouped output by 'ORIGIN_PT_CODE'. You can override using
the `.groups` argument.Let’s check the content of newly created odbus6_9 using datatable() function.
datatable(odbus6_9)Warning in instance$preRenderHook(instance): It seems your data is too big for
client-side DataTables. You may consider server-side processing:
https://rstudio.github.io/DT/server.htmlWe will save the output in rds format for future used.
write_rds(odbus6_9, "../data/rds/odbus6_9.rds")4.2 Geospatial Data Wrangling
4.2.2 Combining Bus Stop and MPSZ
Code chunk below populates the planning subzone code (i.e. SUBZONE_C) of mpsz sf data frame into busstop sf data frame.
busstop_mpsz <- st_intersection(busstop, mpsz) %>%
select(BUS_STOP_N, SUBZONE_C) %>%
st_drop_geometry()Warning: attribute variables are assumed to be spatially constant throughout
all geometriesdatatable(busstop_mpsz)We will save the output into rds format.
write_rds(busstop_mpsz, "../data/rds/busstop_mpsz.rds") Next, we will append the planning subzone code from busstop_mpsz data frame onto odbus6_9 data frame.
od_data <- left_join(odbus6_9 , busstop_mpsz,
by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE,
ORIGIN_SZ = SUBZONE_C,
DESTIN_BS = DESTINATION_PT_CODE)Warning in left_join(odbus6_9, busstop_mpsz, by = c(ORIGIN_PT_CODE = "BUS_STOP_N")): Detected an unexpected many-to-many relationship between `x` and `y`.
ℹ Row 55491 of `x` matches multiple rows in `y`.
ℹ Row 161 of `y` matches multiple rows in `x`.
ℹ If a many-to-many relationship is expected, set `relationship =
"many-to-many"` to silence this warning.Before continue, it is a good practice for us to check for duplicating records.
duplicate <- od_data %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()
duplicate# A tibble: 976 × 4
ORIGIN_BS DESTIN_BS TRIPS ORIGIN_SZ
<chr> <fct> <dbl> <chr>
1 22501 22009 3 JWSZ09
2 22501 22009 3 JWSZ09
3 22501 22451 85 JWSZ09
4 22501 22451 85 JWSZ09
5 22501 22469 18 JWSZ09
6 22501 22469 18 JWSZ09
7 22501 22479 29 JWSZ09
8 22501 22479 29 JWSZ09
9 22501 22509 3 JWSZ09
10 22501 22509 3 JWSZ09
# ℹ 966 more rowsSince we have found duplicated records as seen in the table above, we will use the code chunk below to retain the unique records only.
od_data <- unique(od_data)It is a good practice to confirm if the duplicating records issue has been addressed fully.
duplicate <- od_data %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()
duplicate# A tibble: 0 × 4
# ℹ 4 variables: ORIGIN_BS <chr>, DESTIN_BS <fct>, TRIPS <dbl>, ORIGIN_SZ <chr>Now there is no more duplicated data. We can continue with updating the od_data data frame with planning subzone codes.
od_data <- left_join(od_data , busstop_mpsz,
by = c("DESTIN_BS" = "BUS_STOP_N")) Warning in left_join(od_data, busstop_mpsz, by = c(DESTIN_BS = "BUS_STOP_N")): Detected an unexpected many-to-many relationship between `x` and `y`.
ℹ Row 74 of `x` matches multiple rows in `y`.
ℹ Row 1379 of `y` matches multiple rows in `x`.
ℹ If a many-to-many relationship is expected, set `relationship =
"many-to-many"` to silence this warning.Once again, let’s check the duplicates
duplicate <- od_data %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()
duplicate# A tibble: 1,256 × 5
ORIGIN_BS DESTIN_BS TRIPS ORIGIN_SZ SUBZONE_C
<chr> <chr> <dbl> <chr> <chr>
1 1012 82221 1 <NA> GLSZ05
2 1012 82221 1 <NA> GLSZ05
3 1112 51071 49 <NA> CCSZ01
4 1112 51071 49 <NA> CCSZ01
5 1112 53041 4 <NA> BSSZ01
6 1112 53041 4 <NA> BSSZ01
7 1112 82221 1 <NA> GLSZ05
8 1112 82221 1 <NA> GLSZ05
9 1113 51071 2 <NA> CCSZ01
10 1113 51071 2 <NA> CCSZ01
# ℹ 1,246 more rowsDuplicate issue still exists that needs to be addressed.
od_data <- unique(od_data)od_data <- od_data %>%
rename(DESTIN_SZ = SUBZONE_C) %>%
drop_na() %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarise(MORNING_PEAK = sum(TRIPS))`summarise()` has grouped output by 'ORIGIN_SZ'. You can override using the
`.groups` argument.Now that we have prepared the data and addressed the issues, we can now save the output into rds file format.
write_rds(od_data, "../data/rds/od_data_fii.rds")5.0 Visualising Spatial Interaction
In this section, we will explore how to prepare a desire line by using stplanr package. In an Origin-Destination (O-D) study, desire lines are used to determine the travel pattern of an area or city. They represent the number of people going from one origin to another destination.
5.1 Removing intra-zonal flows
Desire lines plot between one origin and one destination. It means it cannot represent intra-zonal flows where origin and destination belong to the same spatial unit (in our case, same subzone or planning area). Hence, we will first need to remove intra-zonal flows from our data.
od_data_fij <- od_data[od_data$ORIGIN_SZ!=od_data$DESTIN_SZ,]Next, we will save the output in a rds file format.
write_rds(od_data_fij, "../data/rds/od_data_fij.rds")5.2 Creating Desire Lines
To create desire lines, we will make use of od2line() function from stplanr package. This package takes in the origin and destination of a flow and transform it into a linestring.
flowLine <- od2line(flow = od_data_fij,
zones = mpsz,
zone_code = "SUBZONE_C")Creating centroids representing desire line start and end points.The comment suggests that centroids are used to represent the start and end points.
Let’s save the output into the rds file format.
write_rds(flowLine, "../data/rds/flowLine.rds")5.3 Visualising the Desire Lines
tm_shape(mpsz) +
tm_polygons() +
flowLine %>%
tm_shape() +
tm_lines(lwd = "MORNING_PEAK",
style = "quantile",
scale = c(0.1, 1, 3, 5, 7, 10),
n = 6)
6.0 Computing Distance Matrix
In spatial interaction, a distance matrix is a table that shows the distance between pairs of locations. For example, in the table below we can see an Euclidean distance of 3926.0025 between MESZ01 and RVSZ05, of 3939.1079 between MESZ01 and SRSZ01, and so on. By definition, an location’s distance from itself, which is shown in the main diagonal of the table, is 0. In this section, we will conduct additional data preparation necessary to compute distance matrix to run spatial interaction modelling.
6.1 Converting from sf data.table to SpatialPolygonsDataFrame
There are at least two ways to compute the required distance matrix. One is based on sf and the other is based on sp. Past experience shown that computing distance matrix by using sf function took relatively longer time that sp method especially the data set is large. In view of this, sp method is used in the code chunks below.
First as.Spatial() will be used to convert mpsz from sf tibble data frame to SpatialPolygonsDataFrame of sp object as shown in the code chunk below.
mpsz_sp <- as(mpsz, "Spatial")
mpsz_spclass : SpatialPolygonsDataFrame
features : 332
extent : 2667.538, 56396.44, 15748.72, 50256.33 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 6
names : SUBZONE_N, SUBZONE_C, PLN_AREA_N, PLN_AREA_C, REGION_N, REGION_C
min values : ADMIRALTY, AMSZ01, ANG MO KIO, AM, CENTRAL REGION, CR
max values : YUNNAN, YSSZ09, YISHUN, YS, WEST REGION, WR 6.2 Computing Distance Matrix
Next, spDists() of sp package will be used to compute the Euclidean distance between the centroids of the planning subzones.
dist <- spDists(mpsz_sp,
longlat = FALSE)head(dist, n=c(10, 10)) [,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 0.000 3926.0025 3939.108 20252.964 2989.9839 1431.330 19211.836
[2,] 3926.003 0.0000 305.737 16513.865 951.8314 5254.066 16242.523
[3,] 3939.108 305.7370 0.000 16412.062 1045.9088 5299.849 16026.146
[4,] 20252.964 16513.8648 16412.062 0.000 17450.3044 21665.795 7229.017
[5,] 2989.984 951.8314 1045.909 17450.304 0.0000 4303.232 17020.916
[6,] 1431.330 5254.0664 5299.849 21665.795 4303.2323 0.000 20617.082
[7,] 19211.836 16242.5230 16026.146 7229.017 17020.9161 20617.082 0.000
[8,] 14960.942 12749.4101 12477.871 11284.279 13336.0421 16281.453 5606.082
[9,] 7515.256 7934.8082 7649.776 18427.503 7801.6163 8403.896 14810.930
[10,] 6391.342 4975.0021 4669.295 15469.566 5226.8731 7707.091 13111.391
[,8] [,9] [,10]
[1,] 14960.942 7515.256 6391.342
[2,] 12749.410 7934.808 4975.002
[3,] 12477.871 7649.776 4669.295
[4,] 11284.279 18427.503 15469.566
[5,] 13336.042 7801.616 5226.873
[6,] 16281.453 8403.896 7707.091
[7,] 5606.082 14810.930 13111.391
[8,] 0.000 9472.024 8575.490
[9,] 9472.024 0.000 3780.800
[10,] 8575.490 3780.800 0.000Notice that the output dist is a matrix object class of R. Also notice that the column heanders and row headers are not labeled with the planning subzone codes. We need to carry out additional data preparation steps to tidy this data up.
6.3 Labelling Column and Row Headers of Distance Matrix
First, we will create a list sorted according to the the distance matrix by planning sub-zone code.
sz_names <- mpsz$SUBZONE_CNext we will attach SUBZONE_C to row and column for distance matrix matching ahead
colnames(dist) <- paste0(sz_names)
rownames(dist) <- paste0(sz_names)6.4 Pivoting Distance Value by SUBZONE_C
Next, we will pivot the distance matrix into a long table by using the row and column subzone codes as show in the code chunk below.
distPair <- melt(dist) %>%
rename(dist = value)
head(distPair, 10) Var1 Var2 dist
1 MESZ01 MESZ01 0.000
2 RVSZ05 MESZ01 3926.003
3 SRSZ01 MESZ01 3939.108
4 WISZ01 MESZ01 20252.964
5 MUSZ02 MESZ01 2989.984
6 MPSZ05 MESZ01 1431.330
7 WISZ03 MESZ01 19211.836
8 WISZ02 MESZ01 14960.942
9 SISZ02 MESZ01 7515.256
10 SISZ01 MESZ01 6391.342Notice that the within zone distance is 0.
6.5 Updating Intra-zonal Distances
In this section, we are going to append a constant value to replace the intra-zonal distance of 0. First, we will select and find out the minimum value of the distance by using summary().
distPair %>%
filter(dist > 0) %>%
summary() Var1 Var2 dist
MESZ01 : 331 MESZ01 : 331 Min. : 173.8
RVSZ05 : 331 RVSZ05 : 331 1st Qu.: 7149.5
SRSZ01 : 331 SRSZ01 : 331 Median :11890.0
WISZ01 : 331 WISZ01 : 331 Mean :12229.4
MUSZ02 : 331 MUSZ02 : 331 3rd Qu.:16401.7
MPSZ05 : 331 MPSZ05 : 331 Max. :49894.4
(Other):107906 (Other):107906 Next, a constant distance value of 50m is added into intra-zones distance.
distPair$dist <- ifelse(distPair$dist == 0,
50, distPair$dist)
distPair %>%
summary() Var1 Var2 dist
MESZ01 : 332 MESZ01 : 332 Min. : 50
RVSZ05 : 332 RVSZ05 : 332 1st Qu.: 7097
SRSZ01 : 332 SRSZ01 : 332 Median :11864
WISZ01 : 332 WISZ01 : 332 Mean :12193
MUSZ02 : 332 MUSZ02 : 332 3rd Qu.:16388
MPSZ05 : 332 MPSZ05 : 332 Max. :49894
(Other):108232 (Other):108232 The code chunk below is used to rename the origin and destination fields.
distPair <- distPair %>%
rename(orig = Var1,
dest = Var2)Lastly, the code chunk below is used to save the dataframe into rds file format
write_rds(distPair, "../data/rds/distPair.rds") 7.0 Preparing the Flow Data
Firstly, we will compute the total passenger trip between and within planning subzones by using the code chunk below. The output is called flow_data.
flow_data <- od_data_fij %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarize(TRIPS = sum(MORNING_PEAK)) `summarise()` has grouped output by 'ORIGIN_SZ'. You can override using the
`.groups` argument.Let’s look at some of the data rows.
head(flow_data, 10)# A tibble: 10 × 3
# Groups: ORIGIN_SZ [1]
ORIGIN_SZ DESTIN_SZ TRIPS
<chr> <chr> <dbl>
1 AMSZ01 AMSZ02 8289
2 AMSZ01 AMSZ03 8971
3 AMSZ01 AMSZ04 2252
4 AMSZ01 AMSZ05 6136
5 AMSZ01 AMSZ06 2148
6 AMSZ01 AMSZ07 1620
7 AMSZ01 AMSZ08 1925
8 AMSZ01 AMSZ09 1773
9 AMSZ01 AMSZ10 63
10 AMSZ01 AMSZ11 5427.1 Separating intra-flow from passenger volume df
Code chunk below is used to add two new fields in flow_data dataframe namely FlowNoIntra and offset.
flow_data$FlowNoIntra <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0, flow_data$TRIPS)
flow_data$offset <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0.000001, 1)7.2 Combining passenger volume data with distance value
Before we can join flow_data and distPair, we need to convert data value type of ORIGIN_SZ and DESTIN_SZ fields of flow_data dataframe into factor data type.
flow_data$ORIGIN_SZ <- as.factor(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.factor(flow_data$DESTIN_SZ)Now, left_join() of dplyr will be used to flow_data dataframe and distPair dataframe. The output is called flow_data1.
flow_data1 <- flow_data %>%
left_join (distPair,
by = c("ORIGIN_SZ" = "orig",
"DESTIN_SZ" = "dest"))8.0 Preparing Origin and Destination Attributes
8.1 Importing population data
Firstly, we will import the population data.
pop <- read_csv("../data/aspatial/pop.csv")Rows: 332 Columns: 5
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (2): PA, SZ
dbl (3): AGE7_12, AGE13_24, AGE25_64
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.Next, we will do a left_join to pop data frame with mpsz. The output will be a sf object where each polygon in mpsz will be assigned a population value.
pop <- pop %>%
left_join(mpsz,
by = c("PA" = "PLN_AREA_N",
"SZ" = "SUBZONE_N")) %>%
select(1:6) %>%
rename(SZ_NAME = SZ,
SZ = SUBZONE_C)Next, we will need to do another left_join() with flow_data1 that we have prepared earlier to prepare both origin and destination attributes.
flow_data1 <- flow_data1 %>%
left_join(pop,
by = c(ORIGIN_SZ = "SZ")) %>%
rename(ORIGIN_AGE7_12 = AGE7_12,
ORIGIN_AGE13_24 = AGE13_24,
ORIGIN_AGE25_64 = AGE25_64) %>%
select(-c(PA, SZ_NAME))flow_data1 <- flow_data1 %>%
left_join(pop,
by = c(DESTIN_SZ = "SZ")) %>%
rename(DESTIN_AGE7_12 = AGE7_12,
DESTIN_AGE13_24 = AGE13_24,
DESTIN_AGE25_64 = AGE25_64) %>%
select(-c(PA, SZ_NAME))We will called the output data file SIM_data. it is in rds data file format.
write_rds(flow_data1, "../data/rds/flow_data_6-9.rds")
SIM_data <- read_rds("../data/rds/flow_data_6-9.rds")9.0 Calibrating Spatial Interaction Models
In this section, we explore how to calibrate Spatial Interaction Models by using Poisson Regression method.
9.1 Visualising the Dependent Variables
Firstly, let us plot the distribution of the dependent variable (i.e. TRIPS) by using histogram method by using the code chunk below.
ggplot(data = SIM_data,
aes(x = TRIPS)) +
geom_histogram()`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Notice that the distribution is highly skewed and not resemble bell shape or also known as normal distribution.
Next, let us visualise the relation between the dependent variable and one of the key independent variable in Spatial Interaction Model, namely distance.
ggplot(data = SIM_data,
aes(x = dist,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)`geom_smooth()` using formula = 'y ~ x'
Notice that their relationship hardly resemble linear relationship.
On the other hand, if we plot the scatter plot by using the log transformed version of both variables, we can see that their relationship is more resemble linear relationship.
ggplot(data = SIM_data,
aes(x = log(dist),
y = log(TRIPS))) +
geom_point() +
geom_smooth(method = lm)`geom_smooth()` using formula = 'y ~ x'
9.2 Log Transformation
Since Poisson Regression is based of log and log 0 is undefined, it is important for us to ensure that no 0 values in the explanatory variables.
In the code chunk below, summary() of Base R is used to compute the summary statistics of all variables in SIM_data data frame.
summary(SIM_data) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Length:14471 Length:14471 Min. : 1.0 Min. : 1.0
Class :character Class :character 1st Qu.: 14.0 1st Qu.: 14.0
Mode :character Mode :character Median : 73.0 Median : 73.0
Mean : 855.1 Mean : 855.1
3rd Qu.: 393.0 3rd Qu.: 393.0
Max. :148274.0 Max. :148274.0
offset dist ORIGIN_AGE7_12 ORIGIN_AGE13_24 ORIGIN_AGE25_64
Min. :1 Min. : 173.8 Min. : 0 Min. : 0 Min. : 0
1st Qu.:1 1st Qu.: 3498.5 1st Qu.: 240 1st Qu.: 460 1st Qu.: 2210
Median :1 Median : 6181.8 Median : 700 Median : 1350 Median : 7030
Mean :1 Mean : 7004.2 Mean :1034 Mean : 2274 Mean :10516
3rd Qu.:1 3rd Qu.: 9796.4 3rd Qu.:1500 3rd Qu.: 3260 3rd Qu.:15770
Max. :1 Max. :26135.8 Max. :6340 Max. :16380 Max. :74610
DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
Min. : 0 Min. : 0 Min. : 0
1st Qu.: 250 1st Qu.: 460 1st Qu.: 2210
Median : 720 Median : 1430 Median : 7030
Mean :1036 Mean : 2296 Mean :10605
3rd Qu.:1500 3rd Qu.: 3260 3rd Qu.:15830
Max. :6340 Max. :16380 Max. :74610 The print report above reveals that variables ORIGIN_AGE7_12, ORIGIN_AGE13_24, ORIGIN_AGE25_64,DESTIN_AGE7_12, DESTIN_AGE13_24, DESTIN_AGE25_64 consist of 0 values.
In view of this, code chunk below will be used to replace zero values to 0.99.
SIM_data$DESTIN_AGE7_12 <- ifelse(
SIM_data$DESTIN_AGE7_12 == 0,
0.99, SIM_data$DESTIN_AGE7_12)
SIM_data$DESTIN_AGE13_24 <- ifelse(
SIM_data$DESTIN_AGE13_24 == 0,
0.99, SIM_data$DESTIN_AGE13_24)
SIM_data$DESTIN_AGE25_64 <- ifelse(
SIM_data$DESTIN_AGE25_64 == 0,
0.99, SIM_data$DESTIN_AGE25_64)
SIM_data$ORIGIN_AGE7_12 <- ifelse(
SIM_data$ORIGIN_AGE7_12 == 0,
0.99, SIM_data$ORIGIN_AGE7_12)
SIM_data$ORIGIN_AGE13_24 <- ifelse(
SIM_data$ORIGIN_AGE13_24 == 0,
0.99, SIM_data$ORIGIN_AGE13_24)
SIM_data$ORIGIN_AGE25_64 <- ifelse(
SIM_data$ORIGIN_AGE25_64 == 0,
0.99, SIM_data$ORIGIN_AGE25_64)Let’s summarise the new data
summary(SIM_data) ORIGIN_SZ DESTIN_SZ TRIPS FlowNoIntra
Length:14471 Length:14471 Min. : 1.0 Min. : 1.0
Class :character Class :character 1st Qu.: 14.0 1st Qu.: 14.0
Mode :character Mode :character Median : 73.0 Median : 73.0
Mean : 855.1 Mean : 855.1
3rd Qu.: 393.0 3rd Qu.: 393.0
Max. :148274.0 Max. :148274.0
offset dist ORIGIN_AGE7_12 ORIGIN_AGE13_24
Min. :1 Min. : 173.8 Min. : 0.99 Min. : 0.99
1st Qu.:1 1st Qu.: 3498.5 1st Qu.: 240.00 1st Qu.: 460.00
Median :1 Median : 6181.8 Median : 700.00 Median : 1350.00
Mean :1 Mean : 7004.2 Mean :1034.15 Mean : 2274.15
3rd Qu.:1 3rd Qu.: 9796.4 3rd Qu.:1500.00 3rd Qu.: 3260.00
Max. :1 Max. :26135.8 Max. :6340.00 Max. :16380.00
ORIGIN_AGE25_64 DESTIN_AGE7_12 DESTIN_AGE13_24 DESTIN_AGE25_64
Min. : 0.99 Min. : 0.99 Min. : 0.99 Min. : 0.99
1st Qu.: 2210.00 1st Qu.: 250.00 1st Qu.: 460.00 1st Qu.: 2210.00
Median : 7030.00 Median : 720.00 Median : 1430.00 Median : 7030.00
Mean :10516.44 Mean :1035.72 Mean : 2296.06 Mean :10604.87
3rd Qu.:15770.00 3rd Qu.:1500.00 3rd Qu.: 3260.00 3rd Qu.:15830.00
Max. :74610.00 Max. :6340.00 Max. :16380.00 Max. :74610.00 Notice that all the 0 values have been replaced by 0.99.
9.3 Unconstrained Spatial Interaction Model
In this section, we will calibrate an unconstrained spatial interaction model by using glm() function. The explanatory variables are origin population by different age cohort, destination population by different age cohort (i.e. ORIGIN_AGE25_64) and distance between origin and destination in km (i.e. dist).
uncSIM <- glm(formula = TRIPS ~
log(ORIGIN_AGE25_64) +
log(DESTIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
uncSIM
Call: glm(formula = TRIPS ~ log(ORIGIN_AGE25_64) + log(DESTIN_AGE25_64) +
log(dist), family = poisson(link = "log"), data = SIM_data,
na.action = na.exclude)
Coefficients:
(Intercept) log(ORIGIN_AGE25_64) log(DESTIN_AGE25_64)
16.99076 0.22371 0.01103
log(dist)
-1.49596
Degrees of Freedom: 14470 Total (i.e. Null); 14467 Residual
Null Deviance: 47090000
Residual Deviance: 26270000 AIC: 263600009.3.1 R-squared function
In order to measure how much variation of the trips can be accounted by the model we will write a function to calculate R-Squared value as shown below.
CalcRSquared <- function(observed,estimated){
r <- cor(observed,estimated)
R2 <- r^2
R2
}Next, we will compute the R-squared of the unconstrained SIM by using the code chunk below.
CalcRSquared(uncSIM$data$TRIPS, uncSIM$fitted.values)[1] 0.1674135r2_mcfadden(uncSIM)# R2 for Generalized Linear Regression
R2: 0.441
adj. R2: 0.4419.4 Origin Constrained Spatial Interaction Model
In this section, we will calibrate an origin constrained SIM. For origin constrained SIM, only explanatory variables representing the attractiveness at the destinations will be used. This is because such models emphasize the limitations or capacities of the origins rather than the demand or attractiveness of the destinations. The capacity or limitation at the origin sites determines the potential for generating interactions or flows.
orcSIM <- glm(formula = TRIPS ~
ORIGIN_SZ +
log(DESTIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
summary(orcSIM)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + log(DESTIN_AGE25_64) + log(dist),
family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 1.987e+01 4.770e-03 4166.411 < 2e-16 ***
ORIGIN_SZAMSZ02 7.160e-01 4.683e-03 152.904 < 2e-16 ***
ORIGIN_SZAMSZ03 3.862e-01 4.873e-03 79.258 < 2e-16 ***
ORIGIN_SZAMSZ04 -6.846e-02 5.306e-03 -12.904 < 2e-16 ***
ORIGIN_SZAMSZ05 -2.426e-01 5.954e-03 -40.750 < 2e-16 ***
ORIGIN_SZAMSZ06 1.022e-01 5.307e-03 19.257 < 2e-16 ***
ORIGIN_SZAMSZ07 -1.119e+00 9.793e-03 -114.308 < 2e-16 ***
ORIGIN_SZAMSZ08 -6.525e-01 9.213e-03 -70.829 < 2e-16 ***
ORIGIN_SZAMSZ09 1.377e-01 5.629e-03 24.456 < 2e-16 ***
ORIGIN_SZAMSZ10 4.212e-01 4.907e-03 85.834 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.352e+00 1.302e-02 -103.836 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.456e+00 1.111e-02 -131.089 < 2e-16 ***
ORIGIN_SZBDSZ01 1.371e+00 4.574e-03 299.666 < 2e-16 ***
ORIGIN_SZBDSZ02 9.665e-01 5.291e-03 182.663 < 2e-16 ***
ORIGIN_SZBDSZ03 1.183e+00 4.799e-03 246.605 < 2e-16 ***
ORIGIN_SZBDSZ04 2.020e+00 4.123e-03 489.880 < 2e-16 ***
ORIGIN_SZBDSZ05 1.048e+00 4.820e-03 217.428 < 2e-16 ***
ORIGIN_SZBDSZ06 1.277e+00 4.876e-03 261.937 < 2e-16 ***
ORIGIN_SZBDSZ07 -5.256e-01 9.903e-03 -53.079 < 2e-16 ***
ORIGIN_SZBDSZ08 -3.868e-01 9.240e-03 -41.859 < 2e-16 ***
ORIGIN_SZBKSZ01 -3.459e-01 6.703e-03 -51.602 < 2e-16 ***
ORIGIN_SZBKSZ02 2.298e-01 5.352e-03 42.938 < 2e-16 ***
ORIGIN_SZBKSZ03 5.502e-01 5.091e-03 108.081 < 2e-16 ***
ORIGIN_SZBKSZ04 -3.136e-01 6.273e-03 -49.987 < 2e-16 ***
ORIGIN_SZBKSZ05 -2.838e-01 6.547e-03 -43.341 < 2e-16 ***
ORIGIN_SZBKSZ06 -1.650e-01 5.971e-03 -27.628 < 2e-16 ***
ORIGIN_SZBKSZ07 5.456e-01 4.609e-03 118.381 < 2e-16 ***
ORIGIN_SZBKSZ08 4.522e-03 5.411e-03 0.836 0.403270
ORIGIN_SZBKSZ09 -7.805e-02 5.859e-03 -13.320 < 2e-16 ***
ORIGIN_SZBLSZ01 -1.646e+00 1.505e-02 -109.411 < 2e-16 ***
ORIGIN_SZBLSZ02 -1.969e+00 1.935e-02 -101.754 < 2e-16 ***
ORIGIN_SZBLSZ03 -2.831e+00 4.620e-02 -61.282 < 2e-16 ***
ORIGIN_SZBLSZ04 -1.523e+00 2.341e-02 -65.061 < 2e-16 ***
ORIGIN_SZBMSZ01 9.162e-02 5.508e-03 16.632 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.383e+00 6.964e-03 -198.608 < 2e-16 ***
ORIGIN_SZBMSZ03 -6.753e-01 5.844e-03 -115.568 < 2e-16 ***
ORIGIN_SZBMSZ04 -5.975e-01 5.381e-03 -111.050 < 2e-16 ***
ORIGIN_SZBMSZ05 -3.117e+00 1.701e-02 -183.286 < 2e-16 ***
ORIGIN_SZBMSZ06 -3.113e+00 1.832e-02 -169.918 < 2e-16 ***
ORIGIN_SZBMSZ07 -7.169e-01 5.949e-03 -120.520 < 2e-16 ***
ORIGIN_SZBMSZ08 -8.906e-01 5.955e-03 -149.544 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.352e+00 8.846e-03 -152.846 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.709e+00 9.149e-03 -186.753 < 2e-16 ***
ORIGIN_SZBMSZ11 -1.147e+00 6.679e-03 -171.690 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.293e+00 9.529e-03 -135.725 < 2e-16 ***
ORIGIN_SZBMSZ13 -3.687e-01 6.084e-03 -60.610 < 2e-16 ***
ORIGIN_SZBMSZ14 -9.309e-01 6.713e-03 -138.680 < 2e-16 ***
ORIGIN_SZBMSZ15 -6.446e-01 6.180e-03 -104.296 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.542e+00 9.459e-03 -163.043 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.631e+00 1.585e-02 -102.955 < 2e-16 ***
ORIGIN_SZBPSZ01 1.983e-01 5.708e-03 34.735 < 2e-16 ***
ORIGIN_SZBPSZ02 -3.032e-01 6.537e-03 -46.383 < 2e-16 ***
ORIGIN_SZBPSZ03 -9.632e-02 6.370e-03 -15.122 < 2e-16 ***
ORIGIN_SZBPSZ04 4.968e-01 5.162e-03 96.237 < 2e-16 ***
ORIGIN_SZBPSZ05 5.887e-01 4.711e-03 124.972 < 2e-16 ***
ORIGIN_SZBPSZ06 -1.115e+00 9.511e-03 -117.231 < 2e-16 ***
ORIGIN_SZBPSZ07 -4.329e-01 8.907e-03 -48.600 < 2e-16 ***
ORIGIN_SZBSSZ01 1.363e-01 5.843e-03 23.321 < 2e-16 ***
ORIGIN_SZBSSZ02 4.209e-01 4.992e-03 84.319 < 2e-16 ***
ORIGIN_SZBSSZ03 -2.505e-01 5.546e-03 -45.163 < 2e-16 ***
ORIGIN_SZBTSZ01 1.444e-01 6.019e-03 23.987 < 2e-16 ***
ORIGIN_SZBTSZ02 -5.337e-01 8.237e-03 -64.793 < 2e-16 ***
ORIGIN_SZBTSZ03 -3.786e-01 7.043e-03 -53.754 < 2e-16 ***
ORIGIN_SZBTSZ04 -1.150e+00 1.060e-02 -108.559 < 2e-16 ***
ORIGIN_SZBTSZ05 -1.082e+00 1.212e-02 -89.274 < 2e-16 ***
ORIGIN_SZBTSZ06 -1.207e+00 9.603e-03 -125.683 < 2e-16 ***
ORIGIN_SZBTSZ07 -2.344e+00 1.427e-02 -164.290 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.217e+00 1.108e-02 -109.767 < 2e-16 ***
ORIGIN_SZCBSZ01 -1.242e+00 5.484e-02 -22.641 < 2e-16 ***
ORIGIN_SZCCSZ01 -9.023e-01 1.398e-02 -64.556 < 2e-16 ***
ORIGIN_SZCHSZ01 -3.764e-02 1.214e-02 -3.101 0.001930 **
ORIGIN_SZCHSZ02 -5.426e-01 8.413e-03 -64.502 < 2e-16 ***
ORIGIN_SZCHSZ03 1.559e+00 6.373e-03 244.612 < 2e-16 ***
ORIGIN_SZCKSZ01 1.528e-01 5.263e-03 29.027 < 2e-16 ***
ORIGIN_SZCKSZ02 5.729e-01 5.369e-03 106.695 < 2e-16 ***
ORIGIN_SZCKSZ03 8.313e-01 4.611e-03 180.288 < 2e-16 ***
ORIGIN_SZCKSZ04 1.391e+00 4.646e-03 299.420 < 2e-16 ***
ORIGIN_SZCKSZ05 1.041e+00 5.393e-03 193.068 < 2e-16 ***
ORIGIN_SZCKSZ06 4.753e-01 7.466e-03 63.662 < 2e-16 ***
ORIGIN_SZCLSZ01 -5.802e-01 7.870e-03 -73.729 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.391e+00 1.367e-02 -101.764 < 2e-16 ***
ORIGIN_SZCLSZ03 -8.248e-01 8.215e-03 -100.401 < 2e-16 ***
ORIGIN_SZCLSZ04 8.458e-01 4.578e-03 184.750 < 2e-16 ***
ORIGIN_SZCLSZ05 -1.649e+00 1.479e-02 -111.489 < 2e-16 ***
ORIGIN_SZCLSZ06 9.161e-01 4.326e-03 211.773 < 2e-16 ***
ORIGIN_SZCLSZ07 -2.174e-01 5.721e-03 -38.000 < 2e-16 ***
ORIGIN_SZCLSZ08 2.070e-01 6.075e-03 34.071 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.315e+00 1.664e-02 -79.040 < 2e-16 ***
ORIGIN_SZDTSZ02 -3.907e+00 8.341e-02 -46.836 < 2e-16 ***
ORIGIN_SZDTSZ03 -3.835e+00 7.381e-02 -51.956 < 2e-16 ***
ORIGIN_SZDTSZ13 -2.992e+00 3.129e-02 -95.616 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.534e+00 9.789e-03 -156.679 < 2e-16 ***
ORIGIN_SZGLSZ02 2.602e-01 5.212e-03 49.927 < 2e-16 ***
ORIGIN_SZGLSZ03 1.702e-01 5.532e-03 30.770 < 2e-16 ***
ORIGIN_SZGLSZ04 9.888e-01 4.400e-03 224.722 < 2e-16 ***
ORIGIN_SZGLSZ05 9.517e-01 4.563e-03 208.583 < 2e-16 ***
ORIGIN_SZHGSZ01 3.117e-01 4.845e-03 64.344 < 2e-16 ***
ORIGIN_SZHGSZ02 4.265e-01 4.835e-03 88.207 < 2e-16 ***
ORIGIN_SZHGSZ03 2.887e-01 5.223e-03 55.280 < 2e-16 ***
ORIGIN_SZHGSZ04 9.189e-01 4.405e-03 208.584 < 2e-16 ***
ORIGIN_SZHGSZ05 1.235e+00 4.373e-03 282.399 < 2e-16 ***
ORIGIN_SZHGSZ06 -3.746e-02 5.677e-03 -6.599 4.14e-11 ***
ORIGIN_SZHGSZ07 4.609e-01 4.905e-03 93.968 < 2e-16 ***
ORIGIN_SZHGSZ08 1.873e-01 5.527e-03 33.884 < 2e-16 ***
ORIGIN_SZHGSZ09 -1.540e+00 7.439e-03 -207.013 < 2e-16 ***
ORIGIN_SZHGSZ10 -2.856e+00 4.215e-02 -67.754 < 2e-16 ***
ORIGIN_SZJESZ01 4.099e-01 5.008e-03 81.855 < 2e-16 ***
ORIGIN_SZJESZ02 1.795e-01 5.012e-03 35.821 < 2e-16 ***
ORIGIN_SZJESZ03 8.032e-02 5.370e-03 14.959 < 2e-16 ***
ORIGIN_SZJESZ04 -1.277e+00 1.010e-02 -126.444 < 2e-16 ***
ORIGIN_SZJESZ05 -2.062e+00 1.402e-02 -147.089 < 2e-16 ***
ORIGIN_SZJESZ06 1.755e-01 4.915e-03 35.714 < 2e-16 ***
ORIGIN_SZJESZ07 -1.760e+00 1.186e-02 -148.470 < 2e-16 ***
ORIGIN_SZJESZ08 -8.114e-01 1.179e-02 -68.825 < 2e-16 ***
ORIGIN_SZJESZ09 7.798e-01 5.143e-03 151.637 < 2e-16 ***
ORIGIN_SZJESZ10 -1.041e+00 1.919e-02 -54.228 < 2e-16 ***
ORIGIN_SZJESZ11 -1.419e+00 1.979e-02 -71.707 < 2e-16 ***
ORIGIN_SZJWSZ01 7.403e-01 6.541e-03 113.180 < 2e-16 ***
ORIGIN_SZJWSZ02 1.128e+00 4.591e-03 245.628 < 2e-16 ***
ORIGIN_SZJWSZ03 1.429e+00 4.310e-03 331.602 < 2e-16 ***
ORIGIN_SZJWSZ04 6.889e-01 5.010e-03 137.491 < 2e-16 ***
ORIGIN_SZJWSZ05 -1.550e+00 1.305e-02 -118.788 < 2e-16 ***
ORIGIN_SZJWSZ06 -8.296e-01 1.092e-02 -75.948 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.042e+00 2.778e-02 -73.524 < 2e-16 ***
ORIGIN_SZJWSZ08 2.140e+00 4.214e-03 507.972 < 2e-16 ***
ORIGIN_SZJWSZ09 1.930e+00 4.034e-03 478.362 < 2e-16 ***
ORIGIN_SZKLSZ01 2.575e-01 5.092e-03 50.559 < 2e-16 ***
ORIGIN_SZKLSZ02 -5.904e-01 6.537e-03 -90.322 < 2e-16 ***
ORIGIN_SZKLSZ03 -4.084e-01 6.035e-03 -67.671 < 2e-16 ***
ORIGIN_SZKLSZ04 -2.101e+00 1.211e-02 -173.485 < 2e-16 ***
ORIGIN_SZKLSZ05 -1.106e+00 1.090e-02 -101.528 < 2e-16 ***
ORIGIN_SZKLSZ06 -5.823e+00 1.857e-01 -31.351 < 2e-16 ***
ORIGIN_SZKLSZ07 -1.196e+00 8.722e-03 -137.181 < 2e-16 ***
ORIGIN_SZKLSZ08 -1.722e+00 1.032e-02 -166.835 < 2e-16 ***
ORIGIN_SZLKSZ01 -1.693e+00 3.973e-02 -42.622 < 2e-16 ***
ORIGIN_SZMDSZ01 -1.157e+00 2.857e-02 -40.501 < 2e-16 ***
ORIGIN_SZMDSZ02 -5.123e-01 1.041e-02 -49.210 < 2e-16 ***
ORIGIN_SZMDSZ03 -1.830e+00 1.708e-02 -107.172 < 2e-16 ***
ORIGIN_SZMPSZ01 -5.757e-01 8.534e-03 -67.467 < 2e-16 ***
ORIGIN_SZMPSZ02 -3.293e-01 7.063e-03 -46.619 < 2e-16 ***
ORIGIN_SZMPSZ03 3.265e-01 5.681e-03 57.476 < 2e-16 ***
ORIGIN_SZMUSZ02 -3.947e+00 1.038e-01 -38.037 < 2e-16 ***
ORIGIN_SZNTSZ01 -2.968e+00 3.530e-02 -84.090 < 2e-16 ***
ORIGIN_SZNTSZ02 -3.275e+00 2.341e-02 -139.897 < 2e-16 ***
ORIGIN_SZNTSZ03 -1.036e+00 7.849e-03 -132.034 < 2e-16 ***
ORIGIN_SZNTSZ05 -4.093e+00 4.964e-02 -82.444 < 2e-16 ***
ORIGIN_SZNTSZ06 -4.680e+00 5.575e-02 -83.940 < 2e-16 ***
ORIGIN_SZNVSZ01 3.575e-01 4.688e-03 76.256 < 2e-16 ***
ORIGIN_SZNVSZ02 -6.214e-01 6.783e-03 -91.610 < 2e-16 ***
ORIGIN_SZNVSZ03 -1.035e+00 8.206e-03 -126.139 < 2e-16 ***
ORIGIN_SZNVSZ04 -9.358e-01 9.203e-03 -101.678 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.238e+00 1.687e-02 -132.722 < 2e-16 ***
ORIGIN_SZPGSZ01 -3.636e-01 1.247e-02 -29.163 < 2e-16 ***
ORIGIN_SZPGSZ02 -3.679e-01 7.514e-03 -48.962 < 2e-16 ***
ORIGIN_SZPGSZ03 7.791e-01 4.869e-03 160.021 < 2e-16 ***
ORIGIN_SZPGSZ04 1.293e+00 4.503e-03 287.129 < 2e-16 ***
ORIGIN_SZPGSZ05 5.066e-01 6.010e-03 84.293 < 2e-16 ***
ORIGIN_SZPLSZ01 -5.817e-01 1.211e-02 -48.032 < 2e-16 ***
ORIGIN_SZPLSZ02 -9.541e-01 1.505e-02 -63.402 < 2e-16 ***
ORIGIN_SZPLSZ03 -1.450e+00 3.721e-02 -38.975 < 2e-16 ***
ORIGIN_SZPLSZ04 -2.423e+00 3.706e-02 -65.386 < 2e-16 ***
ORIGIN_SZPLSZ05 -1.659e+00 2.255e-02 -73.571 < 2e-16 ***
ORIGIN_SZPNSZ01 1.580e+00 4.854e-03 325.551 < 2e-16 ***
ORIGIN_SZPNSZ02 7.624e-01 1.130e-02 67.445 < 2e-16 ***
ORIGIN_SZPNSZ03 -1.375e+00 1.947e-02 -70.626 < 2e-16 ***
ORIGIN_SZPNSZ04 -2.083e+00 3.355e-02 -62.086 < 2e-16 ***
ORIGIN_SZPNSZ05 -8.463e-01 2.762e-02 -30.646 < 2e-16 ***
ORIGIN_SZPRSZ01 1.463e-01 1.185e-02 12.352 < 2e-16 ***
ORIGIN_SZPRSZ02 1.347e+00 4.740e-03 284.231 < 2e-16 ***
ORIGIN_SZPRSZ03 1.011e+00 4.830e-03 209.371 < 2e-16 ***
ORIGIN_SZPRSZ04 2.947e-02 7.676e-03 3.839 0.000124 ***
ORIGIN_SZPRSZ05 1.742e+00 4.487e-03 388.273 < 2e-16 ***
ORIGIN_SZPRSZ06 -8.494e-01 1.188e-02 -71.475 < 2e-16 ***
ORIGIN_SZPRSZ07 -2.217e+00 1.639e-02 -135.246 < 2e-16 ***
ORIGIN_SZPRSZ08 4.627e-01 6.450e-03 71.735 < 2e-16 ***
ORIGIN_SZQTSZ01 -2.925e-01 6.903e-03 -42.382 < 2e-16 ***
ORIGIN_SZQTSZ02 -8.224e-01 6.403e-03 -128.443 < 2e-16 ***
ORIGIN_SZQTSZ03 -2.742e-01 5.909e-03 -46.402 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.230e+00 7.550e-03 -162.859 < 2e-16 ***
ORIGIN_SZQTSZ05 -7.428e-01 6.531e-03 -113.729 < 2e-16 ***
ORIGIN_SZQTSZ06 -6.829e-01 6.841e-03 -99.834 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.435e+00 9.703e-03 -147.867 < 2e-16 ***
ORIGIN_SZQTSZ08 -3.395e-01 6.377e-03 -53.234 < 2e-16 ***
ORIGIN_SZQTSZ09 -6.863e-01 7.209e-03 -95.191 < 2e-16 ***
ORIGIN_SZQTSZ10 -2.947e-01 6.705e-03 -43.952 < 2e-16 ***
ORIGIN_SZQTSZ11 -2.151e+00 1.448e-02 -148.558 < 2e-16 ***
ORIGIN_SZQTSZ12 -2.691e+00 1.877e-02 -143.350 < 2e-16 ***
ORIGIN_SZQTSZ13 -4.465e-01 8.051e-03 -55.453 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.766e+00 1.233e-02 -143.207 < 2e-16 ***
ORIGIN_SZQTSZ15 -4.312e-01 1.219e-02 -35.371 < 2e-16 ***
ORIGIN_SZRCSZ01 -1.707e+00 1.267e-02 -134.759 < 2e-16 ***
ORIGIN_SZRCSZ06 -1.110e+00 8.501e-03 -130.546 < 2e-16 ***
ORIGIN_SZRVSZ01 -3.154e+00 3.243e-02 -97.280 < 2e-16 ***
ORIGIN_SZRVSZ02 -3.703e+00 2.777e-02 -133.358 < 2e-16 ***
ORIGIN_SZRVSZ03 -3.344e+00 2.458e-02 -136.004 < 2e-16 ***
ORIGIN_SZRVSZ04 -3.834e+00 5.567e-02 -68.861 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.997e+00 1.659e-02 -180.629 < 2e-16 ***
ORIGIN_SZSBSZ01 2.289e-01 6.549e-03 34.953 < 2e-16 ***
ORIGIN_SZSBSZ02 -5.709e-01 8.312e-03 -68.686 < 2e-16 ***
ORIGIN_SZSBSZ03 9.116e-01 4.865e-03 187.396 < 2e-16 ***
ORIGIN_SZSBSZ04 9.183e-01 5.425e-03 169.277 < 2e-16 ***
ORIGIN_SZSBSZ05 -9.130e-02 6.826e-03 -13.376 < 2e-16 ***
ORIGIN_SZSBSZ06 -1.102e+00 1.721e-02 -64.058 < 2e-16 ***
ORIGIN_SZSBSZ07 -5.964e-01 1.257e-02 -47.452 < 2e-16 ***
ORIGIN_SZSBSZ08 -9.096e-01 1.417e-02 -64.174 < 2e-16 ***
ORIGIN_SZSBSZ09 -5.758e-01 9.060e-03 -63.555 < 2e-16 ***
ORIGIN_SZSESZ02 1.160e+00 4.514e-03 257.101 < 2e-16 ***
ORIGIN_SZSESZ03 1.181e+00 4.330e-03 272.797 < 2e-16 ***
ORIGIN_SZSESZ04 8.270e-01 4.993e-03 165.617 < 2e-16 ***
ORIGIN_SZSESZ05 -2.483e-01 6.156e-03 -40.341 < 2e-16 ***
ORIGIN_SZSESZ06 9.372e-01 4.839e-03 193.664 < 2e-16 ***
ORIGIN_SZSESZ07 -2.188e+00 1.964e-02 -111.405 < 2e-16 ***
ORIGIN_SZSGSZ01 -7.081e-01 8.721e-03 -81.192 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.219e+00 1.036e-02 -117.649 < 2e-16 ***
ORIGIN_SZSGSZ03 2.171e-01 5.343e-03 40.642 < 2e-16 ***
ORIGIN_SZSGSZ04 4.028e-01 4.975e-03 80.963 < 2e-16 ***
ORIGIN_SZSGSZ05 -1.783e+00 1.092e-02 -163.343 < 2e-16 ***
ORIGIN_SZSGSZ06 4.372e-01 4.746e-03 92.137 < 2e-16 ***
ORIGIN_SZSGSZ07 -7.170e-01 6.553e-03 -109.412 < 2e-16 ***
ORIGIN_SZSKSZ01 2.661e-01 8.687e-03 30.626 < 2e-16 ***
ORIGIN_SZSKSZ02 1.199e+00 5.746e-03 208.588 < 2e-16 ***
ORIGIN_SZSKSZ03 -1.987e-01 8.192e-03 -24.250 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.504e+00 2.763e-02 -54.441 < 2e-16 ***
ORIGIN_SZSKSZ05 -3.753e-01 1.567e-02 -23.952 < 2e-16 ***
ORIGIN_SZSLSZ01 -2.742e+00 3.297e-02 -83.175 < 2e-16 ***
ORIGIN_SZSLSZ04 -2.091e-01 7.811e-03 -26.764 < 2e-16 ***
ORIGIN_SZSRSZ01 -3.036e+00 1.639e-02 -185.276 < 2e-16 ***
ORIGIN_SZTHSZ01 -1.907e+00 4.887e-02 -39.016 < 2e-16 ***
ORIGIN_SZTHSZ03 -1.557e+00 2.244e-02 -69.378 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.634e+00 2.869e-02 -91.787 < 2e-16 ***
ORIGIN_SZTHSZ06 -2.191e+00 1.843e-02 -118.909 < 2e-16 ***
ORIGIN_SZTMSZ01 8.189e-01 5.898e-03 138.855 < 2e-16 ***
ORIGIN_SZTMSZ02 2.363e+00 3.994e-03 591.654 < 2e-16 ***
ORIGIN_SZTMSZ03 1.735e+00 4.307e-03 402.809 < 2e-16 ***
ORIGIN_SZTMSZ04 1.234e+00 5.203e-03 237.220 < 2e-16 ***
ORIGIN_SZTMSZ05 -1.883e-01 1.134e-02 -16.604 < 2e-16 ***
ORIGIN_SZTNSZ01 -2.117e+00 1.294e-02 -163.649 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.953e+00 1.003e-02 -194.676 < 2e-16 ***
ORIGIN_SZTNSZ03 -2.254e+00 1.359e-02 -165.813 < 2e-16 ***
ORIGIN_SZTNSZ04 -6.098e-01 7.548e-03 -80.780 < 2e-16 ***
ORIGIN_SZTPSZ01 -6.947e-01 6.803e-03 -102.119 < 2e-16 ***
ORIGIN_SZTPSZ02 4.354e-01 4.493e-03 96.891 < 2e-16 ***
ORIGIN_SZTPSZ03 -6.871e-01 6.263e-03 -109.710 < 2e-16 ***
ORIGIN_SZTPSZ04 -6.567e-01 5.864e-03 -111.999 < 2e-16 ***
ORIGIN_SZTPSZ05 -5.131e-01 6.238e-03 -82.259 < 2e-16 ***
ORIGIN_SZTPSZ06 -3.195e-01 6.013e-03 -53.129 < 2e-16 ***
ORIGIN_SZTPSZ07 -2.755e-01 6.343e-03 -43.434 < 2e-16 ***
ORIGIN_SZTPSZ08 -1.070e+00 9.744e-03 -109.859 < 2e-16 ***
ORIGIN_SZTPSZ09 -7.583e-01 6.957e-03 -109.002 < 2e-16 ***
ORIGIN_SZTPSZ10 -9.569e-01 7.877e-03 -121.475 < 2e-16 ***
ORIGIN_SZTPSZ11 -2.123e-02 5.717e-03 -3.712 0.000205 ***
ORIGIN_SZTPSZ12 -5.596e-01 6.808e-03 -82.204 < 2e-16 ***
ORIGIN_SZTSSZ01 -1.858e+00 4.792e-02 -38.760 < 2e-16 ***
ORIGIN_SZTSSZ02 1.171e+00 8.351e-03 140.236 < 2e-16 ***
ORIGIN_SZTSSZ03 6.235e-01 8.679e-03 71.837 < 2e-16 ***
ORIGIN_SZTSSZ04 9.407e-01 9.091e-03 103.483 < 2e-16 ***
ORIGIN_SZTSSZ05 1.540e-01 1.524e-02 10.110 < 2e-16 ***
ORIGIN_SZTSSZ06 1.783e+00 1.785e-02 99.894 < 2e-16 ***
ORIGIN_SZWCSZ01 9.661e-01 8.719e-03 110.801 < 2e-16 ***
ORIGIN_SZWCSZ02 -2.128e+00 3.294e-02 -64.614 < 2e-16 ***
ORIGIN_SZWCSZ03 -4.931e+00 1.241e-01 -39.741 < 2e-16 ***
ORIGIN_SZWDSZ01 1.509e+00 4.212e-03 358.263 < 2e-16 ***
ORIGIN_SZWDSZ02 1.096e+00 4.875e-03 224.831 < 2e-16 ***
ORIGIN_SZWDSZ03 1.704e+00 4.566e-03 373.068 < 2e-16 ***
ORIGIN_SZWDSZ04 1.525e+00 5.198e-03 293.289 < 2e-16 ***
ORIGIN_SZWDSZ05 7.276e-01 5.460e-03 133.265 < 2e-16 ***
ORIGIN_SZWDSZ06 9.234e-01 5.288e-03 174.612 < 2e-16 ***
ORIGIN_SZWDSZ07 -6.865e-01 8.560e-03 -80.197 < 2e-16 ***
ORIGIN_SZWDSZ08 -4.019e-01 8.280e-03 -48.532 < 2e-16 ***
ORIGIN_SZWDSZ09 1.648e+00 4.506e-03 365.819 < 2e-16 ***
ORIGIN_SZYSSZ01 -1.148e-01 6.039e-03 -19.006 < 2e-16 ***
ORIGIN_SZYSSZ02 9.402e-01 5.182e-03 181.426 < 2e-16 ***
ORIGIN_SZYSSZ03 1.972e+00 4.401e-03 447.939 < 2e-16 ***
ORIGIN_SZYSSZ04 1.125e+00 4.685e-03 240.242 < 2e-16 ***
ORIGIN_SZYSSZ05 4.050e-01 6.025e-03 67.223 < 2e-16 ***
ORIGIN_SZYSSZ06 -5.788e-01 1.177e-02 -49.178 < 2e-16 ***
ORIGIN_SZYSSZ07 -1.087e+00 1.424e-02 -76.304 < 2e-16 ***
ORIGIN_SZYSSZ08 1.656e-01 6.370e-03 25.992 < 2e-16 ***
ORIGIN_SZYSSZ09 1.137e+00 4.468e-03 254.460 < 2e-16 ***
log(DESTIN_AGE25_64) 2.913e-02 9.125e-05 319.210 < 2e-16 ***
log(dist) -1.665e+00 4.007e-04 -4154.754 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 47094011 on 14470 degrees of freedom
Residual deviance: 16943744 on 14190 degrees of freedom
AIC: 17033444
Number of Fisher Scoring iterations: 6Let’s check the R-square values of origin constrained SIM model this time.
CalcRSquared(orcSIM$data$TRIPS, orcSIM$fitted.values)[1] 0.3990462Notably, R-squared improves from the unconstrained SIM model.
9.5 Destination Constrained Spatial Interaction Model
In this section, we will calibrate an destination constrained SIM. For destination constrained SIM, only explanatory variables which represent how propulsive the origins are will be used. This is because such models emphasize the demand or attractiveness of the destinations rather than the limitations or capacities of the origins. The demand or attractiveness of the destination sites determines the potential for generating interactions or flows.
decSIM <- glm(formula = TRIPS ~
DESTIN_SZ +
log(ORIGIN_AGE25_64) +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
summary(decSIM)
Call:
glm(formula = TRIPS ~ DESTIN_SZ + log(ORIGIN_AGE25_64) + log(dist),
family = poisson(link = "log"), data = SIM_data, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 19.3174878 0.0044874 4304.865 < 2e-16 ***
DESTIN_SZAMSZ02 0.1191704 0.0044773 26.617 < 2e-16 ***
DESTIN_SZAMSZ03 0.1078549 0.0043911 24.562 < 2e-16 ***
DESTIN_SZAMSZ04 -1.0515790 0.0063787 -164.857 < 2e-16 ***
DESTIN_SZAMSZ05 -1.1241092 0.0064528 -174.205 < 2e-16 ***
DESTIN_SZAMSZ06 -1.0692859 0.0064402 -166.032 < 2e-16 ***
DESTIN_SZAMSZ07 -1.5362342 0.0097145 -158.139 < 2e-16 ***
DESTIN_SZAMSZ08 -0.5040655 0.0068854 -73.208 < 2e-16 ***
DESTIN_SZAMSZ09 -0.8920486 0.0065654 -135.872 < 2e-16 ***
DESTIN_SZAMSZ10 0.0580328 0.0045926 12.636 < 2e-16 ***
DESTIN_SZAMSZ11 -0.4055171 0.0086713 -46.765 < 2e-16 ***
DESTIN_SZAMSZ12 0.3630434 0.0050200 72.320 < 2e-16 ***
DESTIN_SZBDSZ01 1.0060750 0.0039763 253.017 < 2e-16 ***
DESTIN_SZBDSZ02 0.2294016 0.0052376 43.799 < 2e-16 ***
DESTIN_SZBDSZ03 0.3255199 0.0047761 68.156 < 2e-16 ***
DESTIN_SZBDSZ04 1.2808827 0.0038167 335.596 < 2e-16 ***
DESTIN_SZBDSZ05 0.9039686 0.0040921 220.906 < 2e-16 ***
DESTIN_SZBDSZ06 0.6176218 0.0046559 132.653 < 2e-16 ***
DESTIN_SZBDSZ07 -0.5303050 0.0096229 -55.109 < 2e-16 ***
DESTIN_SZBDSZ08 -1.2026996 0.0109425 -109.911 < 2e-16 ***
DESTIN_SZBKSZ01 -1.0408499 0.0067517 -154.161 < 2e-16 ***
DESTIN_SZBKSZ02 -0.2277550 0.0056050 -40.634 < 2e-16 ***
DESTIN_SZBKSZ03 -0.6927463 0.0060023 -115.413 < 2e-16 ***
DESTIN_SZBKSZ04 -0.2764020 0.0050053 -55.222 < 2e-16 ***
DESTIN_SZBKSZ05 -0.8937497 0.0066225 -134.957 < 2e-16 ***
DESTIN_SZBKSZ06 -0.9623865 0.0062223 -154.667 < 2e-16 ***
DESTIN_SZBKSZ07 0.0950717 0.0042401 22.422 < 2e-16 ***
DESTIN_SZBKSZ08 -1.2348728 0.0070344 -175.547 < 2e-16 ***
DESTIN_SZBKSZ09 -0.1142258 0.0049953 -22.867 < 2e-16 ***
DESTIN_SZBLSZ01 -0.2105521 0.0070547 -29.846 < 2e-16 ***
DESTIN_SZBLSZ02 0.7245710 0.0065383 110.819 < 2e-16 ***
DESTIN_SZBLSZ03 2.0509336 0.0074325 275.940 < 2e-16 ***
DESTIN_SZBLSZ04 0.4060930 0.0132286 30.698 < 2e-16 ***
DESTIN_SZBMSZ01 -0.0319591 0.0049381 -6.472 9.68e-11 ***
DESTIN_SZBMSZ02 -0.8956122 0.0049560 -180.714 < 2e-16 ***
DESTIN_SZBMSZ03 -1.1137701 0.0057286 -194.424 < 2e-16 ***
DESTIN_SZBMSZ04 -1.0650594 0.0051438 -207.059 < 2e-16 ***
DESTIN_SZBMSZ05 -1.0506824 0.0069501 -151.176 < 2e-16 ***
DESTIN_SZBMSZ06 -2.1441719 0.0131528 -163.020 < 2e-16 ***
DESTIN_SZBMSZ07 -0.2684387 0.0046633 -57.565 < 2e-16 ***
DESTIN_SZBMSZ08 -1.6875691 0.0065033 -259.494 < 2e-16 ***
DESTIN_SZBMSZ09 -3.1074787 0.0152465 -203.816 < 2e-16 ***
DESTIN_SZBMSZ10 -2.2594754 0.0089387 -252.774 < 2e-16 ***
DESTIN_SZBMSZ11 -2.0437882 0.0080887 -252.672 < 2e-16 ***
DESTIN_SZBMSZ12 -1.5042559 0.0080038 -187.943 < 2e-16 ***
DESTIN_SZBMSZ13 -0.5619954 0.0053957 -104.155 < 2e-16 ***
DESTIN_SZBMSZ14 -1.7206419 0.0077676 -221.514 < 2e-16 ***
DESTIN_SZBMSZ15 -1.4869230 0.0071075 -209.204 < 2e-16 ***
DESTIN_SZBMSZ16 -2.1336196 0.0113918 -187.294 < 2e-16 ***
DESTIN_SZBMSZ17 -2.3194650 0.0165782 -139.910 < 2e-16 ***
DESTIN_SZBPSZ01 -0.7515972 0.0056468 -133.101 < 2e-16 ***
DESTIN_SZBPSZ02 -1.7048315 0.0084980 -200.616 < 2e-16 ***
DESTIN_SZBPSZ03 -1.3770138 0.0081263 -169.451 < 2e-16 ***
DESTIN_SZBPSZ04 -0.5249644 0.0059698 -87.937 < 2e-16 ***
DESTIN_SZBPSZ05 0.4444769 0.0040663 109.308 < 2e-16 ***
DESTIN_SZBPSZ06 -0.7688952 0.0078508 -97.938 < 2e-16 ***
DESTIN_SZBPSZ07 -0.0832563 0.0080289 -10.370 < 2e-16 ***
DESTIN_SZBSSZ01 0.0469650 0.0049756 9.439 < 2e-16 ***
DESTIN_SZBSSZ02 -0.6657036 0.0056161 -118.534 < 2e-16 ***
DESTIN_SZBSSZ03 0.1861263 0.0041570 44.774 < 2e-16 ***
DESTIN_SZBTSZ01 0.4792098 0.0043659 109.762 < 2e-16 ***
DESTIN_SZBTSZ02 -0.0951026 0.0068290 -13.926 < 2e-16 ***
DESTIN_SZBTSZ03 0.0668426 0.0054563 12.251 < 2e-16 ***
DESTIN_SZBTSZ04 -1.2625756 0.0108353 -116.524 < 2e-16 ***
DESTIN_SZBTSZ05 -0.1506002 0.0069401 -21.700 < 2e-16 ***
DESTIN_SZBTSZ06 -0.7707905 0.0071082 -108.437 < 2e-16 ***
DESTIN_SZBTSZ07 -1.9349162 0.0110699 -174.791 < 2e-16 ***
DESTIN_SZBTSZ08 -1.4792389 0.0100378 -147.367 < 2e-16 ***
DESTIN_SZCBSZ01 -3.6598718 0.3162427 -11.573 < 2e-16 ***
DESTIN_SZCCSZ01 -0.1832358 0.0081564 -22.465 < 2e-16 ***
DESTIN_SZCHSZ01 -0.0906438 0.0097210 -9.325 < 2e-16 ***
DESTIN_SZCHSZ02 0.2054719 0.0053330 38.529 < 2e-16 ***
DESTIN_SZCHSZ03 2.6595684 0.0040305 659.865 < 2e-16 ***
DESTIN_SZCKSZ01 -0.0016843 0.0049002 -0.344 0.731
DESTIN_SZCKSZ02 -0.4545506 0.0056428 -80.555 < 2e-16 ***
DESTIN_SZCKSZ03 0.6712421 0.0039208 171.201 < 2e-16 ***
DESTIN_SZCKSZ04 -0.3931396 0.0064851 -60.622 < 2e-16 ***
DESTIN_SZCKSZ05 -0.3451862 0.0067912 -50.829 < 2e-16 ***
DESTIN_SZCKSZ06 0.3464208 0.0063562 54.501 < 2e-16 ***
DESTIN_SZCLSZ01 0.2271343 0.0047828 47.490 < 2e-16 ***
DESTIN_SZCLSZ02 -2.0227401 0.0133559 -151.449 < 2e-16 ***
DESTIN_SZCLSZ03 -0.6701371 0.0079127 -84.692 < 2e-16 ***
DESTIN_SZCLSZ04 -0.0265685 0.0047160 -5.634 1.76e-08 ***
DESTIN_SZCLSZ05 -0.8406172 0.0084232 -99.798 < 2e-16 ***
DESTIN_SZCLSZ06 0.2602838 0.0042377 61.421 < 2e-16 ***
DESTIN_SZCLSZ07 -0.4613597 0.0054064 -85.336 < 2e-16 ***
DESTIN_SZCLSZ08 -0.3405745 0.0060605 -56.196 < 2e-16 ***
DESTIN_SZCLSZ09 0.2954783 0.0064320 45.939 < 2e-16 ***
DESTIN_SZDTSZ02 -2.6004589 0.0348415 -74.637 < 2e-16 ***
DESTIN_SZDTSZ03 -1.0453650 0.0144181 -72.504 < 2e-16 ***
DESTIN_SZDTSZ13 -1.7531920 0.0161502 -108.555 < 2e-16 ***
DESTIN_SZGLSZ01 -0.3340462 0.0051940 -64.314 < 2e-16 ***
DESTIN_SZGLSZ02 -0.2202963 0.0050274 -43.819 < 2e-16 ***
DESTIN_SZGLSZ03 0.6533201 0.0040605 160.898 < 2e-16 ***
DESTIN_SZGLSZ04 0.5852771 0.0040616 144.101 < 2e-16 ***
DESTIN_SZGLSZ05 0.6500643 0.0040660 159.876 < 2e-16 ***
DESTIN_SZHGSZ01 0.3288835 0.0039346 83.587 < 2e-16 ***
DESTIN_SZHGSZ02 -0.5011687 0.0054171 -92.516 < 2e-16 ***
DESTIN_SZHGSZ03 -0.9816678 0.0064199 -152.910 < 2e-16 ***
DESTIN_SZHGSZ04 -0.1573402 0.0045848 -34.318 < 2e-16 ***
DESTIN_SZHGSZ05 -0.2540233 0.0048825 -52.027 < 2e-16 ***
DESTIN_SZHGSZ06 -0.7130778 0.0057860 -123.242 < 2e-16 ***
DESTIN_SZHGSZ07 0.1425681 0.0045488 31.342 < 2e-16 ***
DESTIN_SZHGSZ08 -0.1288761 0.0050545 -25.497 < 2e-16 ***
DESTIN_SZHGSZ09 0.1342916 0.0052777 25.445 < 2e-16 ***
DESTIN_SZHGSZ10 -3.3121161 0.0262186 -126.327 < 2e-16 ***
DESTIN_SZJESZ01 0.0216364 0.0050217 4.309 1.64e-05 ***
DESTIN_SZJESZ02 -0.4502278 0.0052909 -85.095 < 2e-16 ***
DESTIN_SZJESZ03 -0.5379992 0.0057901 -92.917 < 2e-16 ***
DESTIN_SZJESZ04 -0.5488314 0.0068410 -80.227 < 2e-16 ***
DESTIN_SZJESZ05 -1.0252722 0.0098376 -104.220 < 2e-16 ***
DESTIN_SZJESZ06 0.3600249 0.0040951 87.917 < 2e-16 ***
DESTIN_SZJESZ07 -1.1741937 0.0081690 -143.738 < 2e-16 ***
DESTIN_SZJESZ08 -0.3232324 0.0079062 -40.884 < 2e-16 ***
DESTIN_SZJESZ09 0.1773240 0.0058326 30.402 < 2e-16 ***
DESTIN_SZJESZ10 1.2098932 0.0069903 173.082 < 2e-16 ***
DESTIN_SZJESZ11 0.8859549 0.0065926 134.386 < 2e-16 ***
DESTIN_SZJWSZ01 -0.0735287 0.0066154 -11.115 < 2e-16 ***
DESTIN_SZJWSZ02 -0.0046865 0.0053345 -0.879 0.380
DESTIN_SZJWSZ03 0.9916788 0.0041074 241.437 < 2e-16 ***
DESTIN_SZJWSZ04 0.8491763 0.0042982 197.565 < 2e-16 ***
DESTIN_SZJWSZ05 -0.3644547 0.0061325 -59.430 < 2e-16 ***
DESTIN_SZJWSZ06 0.3279493 0.0054885 59.752 < 2e-16 ***
DESTIN_SZJWSZ07 -0.4173043 0.0282917 -14.750 < 2e-16 ***
DESTIN_SZJWSZ08 0.8725123 0.0049262 177.118 < 2e-16 ***
DESTIN_SZJWSZ09 1.7499191 0.0035305 495.659 < 2e-16 ***
DESTIN_SZKLSZ01 -0.5783996 0.0055562 -104.100 < 2e-16 ***
DESTIN_SZKLSZ02 -0.7542503 0.0058854 -128.157 < 2e-16 ***
DESTIN_SZKLSZ03 -1.1480172 0.0066481 -172.683 < 2e-16 ***
DESTIN_SZKLSZ04 -1.7364667 0.0088299 -196.657 < 2e-16 ***
DESTIN_SZKLSZ05 -0.6571193 0.0085734 -76.647 < 2e-16 ***
DESTIN_SZKLSZ06 -3.0846942 0.0362084 -85.193 < 2e-16 ***
DESTIN_SZKLSZ07 -1.0843341 0.0067174 -161.421 < 2e-16 ***
DESTIN_SZKLSZ08 -0.7168096 0.0052084 -137.626 < 2e-16 ***
DESTIN_SZLKSZ01 -0.3926093 0.0205594 -19.096 < 2e-16 ***
DESTIN_SZMDSZ01 -0.6873959 0.0200285 -34.321 < 2e-16 ***
DESTIN_SZMDSZ02 -0.8552805 0.0112077 -76.312 < 2e-16 ***
DESTIN_SZMDSZ03 -2.6273198 0.0252255 -104.153 < 2e-16 ***
DESTIN_SZMPSZ01 -0.5827241 0.0078470 -74.261 < 2e-16 ***
DESTIN_SZMPSZ02 -0.5848508 0.0061455 -95.168 < 2e-16 ***
DESTIN_SZMPSZ03 0.2888162 0.0048988 58.957 < 2e-16 ***
DESTIN_SZMUSZ02 -2.6888097 0.0199678 -134.658 < 2e-16 ***
DESTIN_SZNTSZ01 -3.9477895 0.0447770 -88.166 < 2e-16 ***
DESTIN_SZNTSZ02 -1.8818424 0.0108999 -172.648 < 2e-16 ***
DESTIN_SZNTSZ03 -1.4337379 0.0076824 -186.626 < 2e-16 ***
DESTIN_SZNTSZ05 -1.9827445 0.0249764 -79.385 < 2e-16 ***
DESTIN_SZNTSZ06 -2.8268116 0.0428690 -65.941 < 2e-16 ***
DESTIN_SZNVSZ01 -0.4761004 0.0048428 -98.312 < 2e-16 ***
DESTIN_SZNVSZ02 -0.4567368 0.0054397 -83.963 < 2e-16 ***
DESTIN_SZNVSZ03 -0.3742967 0.0055432 -67.524 < 2e-16 ***
DESTIN_SZNVSZ04 -1.7789484 0.0108877 -163.391 < 2e-16 ***
DESTIN_SZNVSZ05 -1.5056497 0.0090744 -165.923 < 2e-16 ***
DESTIN_SZPGSZ01 -1.2450173 0.0158155 -78.721 < 2e-16 ***
DESTIN_SZPGSZ02 -0.7508527 0.0069655 -107.796 < 2e-16 ***
DESTIN_SZPGSZ03 0.2466963 0.0045098 54.702 < 2e-16 ***
DESTIN_SZPGSZ04 0.2183136 0.0046335 47.116 < 2e-16 ***
DESTIN_SZPGSZ05 -0.7375581 0.0079069 -93.281 < 2e-16 ***
DESTIN_SZPLSZ01 -0.0165617 0.0071779 -2.307 0.021 *
DESTIN_SZPLSZ02 -1.2275729 0.0133082 -92.242 < 2e-16 ***
DESTIN_SZPLSZ03 -0.1097448 0.0095959 -11.437 < 2e-16 ***
DESTIN_SZPLSZ04 -1.2147663 0.0094077 -129.125 < 2e-16 ***
DESTIN_SZPLSZ05 -0.2499662 0.0117054 -21.355 < 2e-16 ***
DESTIN_SZPNSZ01 1.0179958 0.0060961 166.990 < 2e-16 ***
DESTIN_SZPNSZ02 2.2918528 0.0064994 352.625 < 2e-16 ***
DESTIN_SZPNSZ03 1.0861145 0.0077155 140.770 < 2e-16 ***
DESTIN_SZPNSZ04 2.8392187 0.0076270 372.261 < 2e-16 ***
DESTIN_SZPNSZ05 2.0314119 0.0117068 173.525 < 2e-16 ***
DESTIN_SZPRSZ01 -0.6909735 0.0086392 -79.981 < 2e-16 ***
DESTIN_SZPRSZ02 0.3340103 0.0053022 62.994 < 2e-16 ***
DESTIN_SZPRSZ03 0.9805752 0.0039615 247.527 < 2e-16 ***
DESTIN_SZPRSZ04 0.0579315 0.0081119 7.142 9.23e-13 ***
DESTIN_SZPRSZ05 0.3755539 0.0049934 75.210 < 2e-16 ***
DESTIN_SZPRSZ06 0.4900142 0.0055218 88.742 < 2e-16 ***
DESTIN_SZPRSZ07 -1.5290486 0.0118420 -129.121 < 2e-16 ***
DESTIN_SZPRSZ08 -0.1807124 0.0065582 -27.555 < 2e-16 ***
DESTIN_SZQTSZ01 -1.0772745 0.0086434 -124.636 < 2e-16 ***
DESTIN_SZQTSZ02 -1.3197772 0.0074726 -176.615 < 2e-16 ***
DESTIN_SZQTSZ03 -1.2512391 0.0069209 -180.792 < 2e-16 ***
DESTIN_SZQTSZ04 -1.1454203 0.0068834 -166.404 < 2e-16 ***
DESTIN_SZQTSZ05 -1.1936837 0.0064953 -183.777 < 2e-16 ***
DESTIN_SZQTSZ06 -1.3285903 0.0067683 -196.297 < 2e-16 ***
DESTIN_SZQTSZ07 -1.6142343 0.0109655 -147.210 < 2e-16 ***
DESTIN_SZQTSZ08 -0.2081946 0.0051794 -40.197 < 2e-16 ***
DESTIN_SZQTSZ09 -0.7425093 0.0061130 -121.464 < 2e-16 ***
DESTIN_SZQTSZ10 -0.0690038 0.0055346 -12.468 < 2e-16 ***
DESTIN_SZQTSZ11 -0.0842897 0.0056434 -14.936 < 2e-16 ***
DESTIN_SZQTSZ12 -0.9234541 0.0082632 -111.755 < 2e-16 ***
DESTIN_SZQTSZ13 0.2103939 0.0057731 36.444 < 2e-16 ***
DESTIN_SZQTSZ14 0.1225968 0.0066223 18.513 < 2e-16 ***
DESTIN_SZQTSZ15 0.6643941 0.0078678 84.445 < 2e-16 ***
DESTIN_SZRCSZ01 -0.7824588 0.0071907 -108.816 < 2e-16 ***
DESTIN_SZRCSZ06 -1.4744760 0.0188871 -78.068 < 2e-16 ***
DESTIN_SZRVSZ01 -2.6526487 0.0162425 -163.315 < 2e-16 ***
DESTIN_SZRVSZ02 -2.6558232 0.0326182 -81.421 < 2e-16 ***
DESTIN_SZRVSZ03 -2.5638290 0.0136476 -187.859 < 2e-16 ***
DESTIN_SZRVSZ04 -2.2999108 0.0155020 -148.362 < 2e-16 ***
DESTIN_SZRVSZ05 -3.7499167 0.0262073 -143.087 < 2e-16 ***
DESTIN_SZSBSZ01 -1.1461594 0.0091462 -125.316 < 2e-16 ***
DESTIN_SZSBSZ02 -1.0429709 0.0077134 -135.215 < 2e-16 ***
DESTIN_SZSBSZ03 0.7170403 0.0043804 163.694 < 2e-16 ***
DESTIN_SZSBSZ04 0.6221775 0.0052894 117.626 < 2e-16 ***
DESTIN_SZSBSZ05 -0.9350093 0.0077024 -121.393 < 2e-16 ***
DESTIN_SZSBSZ06 -1.3858120 0.0221880 -62.458 < 2e-16 ***
DESTIN_SZSBSZ07 0.4060645 0.0181981 22.314 < 2e-16 ***
DESTIN_SZSBSZ08 1.4590891 0.0052348 278.730 < 2e-16 ***
DESTIN_SZSBSZ09 0.5786654 0.0048921 118.286 < 2e-16 ***
DESTIN_SZSESZ02 -0.0743241 0.0049267 -15.086 < 2e-16 ***
DESTIN_SZSESZ03 0.6080690 0.0038671 157.242 < 2e-16 ***
DESTIN_SZSESZ04 -0.5893886 0.0057469 -102.558 < 2e-16 ***
DESTIN_SZSESZ05 -0.2967695 0.0048648 -61.004 < 2e-16 ***
DESTIN_SZSESZ06 -0.2953067 0.0064234 -45.974 < 2e-16 ***
DESTIN_SZSESZ07 -2.7047919 0.0227296 -118.999 < 2e-16 ***
DESTIN_SZSGSZ01 -0.0708513 0.0058798 -12.050 < 2e-16 ***
DESTIN_SZSGSZ02 -0.0331087 0.0052437 -6.314 2.72e-10 ***
DESTIN_SZSGSZ03 -0.1878972 0.0048773 -38.525 < 2e-16 ***
DESTIN_SZSGSZ04 -0.1436643 0.0049574 -28.980 < 2e-16 ***
DESTIN_SZSGSZ05 -2.1277127 0.0100494 -211.725 < 2e-16 ***
DESTIN_SZSGSZ06 0.4639625 0.0039121 118.596 < 2e-16 ***
DESTIN_SZSGSZ07 -0.3923880 0.0053073 -73.933 < 2e-16 ***
DESTIN_SZSISZ01 -1.2823326 0.0257841 -49.733 < 2e-16 ***
DESTIN_SZSKSZ01 0.3506453 0.0072743 48.204 < 2e-16 ***
DESTIN_SZSKSZ02 1.5818816 0.0050613 312.543 < 2e-16 ***
DESTIN_SZSKSZ03 0.2470622 0.0059980 41.191 < 2e-16 ***
DESTIN_SZSKSZ04 -0.1797335 0.0140461 -12.796 < 2e-16 ***
DESTIN_SZSKSZ05 0.7220873 0.0105344 68.545 < 2e-16 ***
DESTIN_SZSLSZ01 -0.2682827 0.0083834 -32.002 < 2e-16 ***
DESTIN_SZSLSZ04 -0.4257565 0.0071360 -59.663 < 2e-16 ***
DESTIN_SZSRSZ01 -2.7348846 0.0130099 -210.216 < 2e-16 ***
DESTIN_SZTHSZ01 -3.3089856 0.0366861 -90.197 < 2e-16 ***
DESTIN_SZTHSZ03 -1.9372568 0.0251019 -77.176 < 2e-16 ***
DESTIN_SZTHSZ04 -2.5939828 0.0213727 -121.369 < 2e-16 ***
DESTIN_SZTHSZ06 -1.9960847 0.0153485 -130.051 < 2e-16 ***
DESTIN_SZTMSZ01 0.4076693 0.0055911 72.914 < 2e-16 ***
DESTIN_SZTMSZ02 1.9259335 0.0034801 553.419 < 2e-16 ***
DESTIN_SZTMSZ03 1.1909948 0.0039856 298.824 < 2e-16 ***
DESTIN_SZTMSZ04 1.5217997 0.0039213 388.081 < 2e-16 ***
DESTIN_SZTMSZ05 1.0042554 0.0056779 176.872 < 2e-16 ***
DESTIN_SZTNSZ01 -0.9786725 0.0071587 -136.711 < 2e-16 ***
DESTIN_SZTNSZ02 -2.1152442 0.0099136 -213.369 < 2e-16 ***
DESTIN_SZTNSZ03 -2.0381861 0.0117106 -174.046 < 2e-16 ***
DESTIN_SZTNSZ04 -0.9321744 0.0071900 -129.648 < 2e-16 ***
DESTIN_SZTPSZ01 -0.6889742 0.0059587 -115.624 < 2e-16 ***
DESTIN_SZTPSZ02 0.3054087 0.0038310 79.721 < 2e-16 ***
DESTIN_SZTPSZ03 -0.7424134 0.0056300 -131.868 < 2e-16 ***
DESTIN_SZTPSZ04 -1.6884798 0.0073617 -229.359 < 2e-16 ***
DESTIN_SZTPSZ05 -1.2242061 0.0058265 -210.111 < 2e-16 ***
DESTIN_SZTPSZ06 -0.8027021 0.0063397 -126.616 < 2e-16 ***
DESTIN_SZTPSZ07 -2.2733422 0.0116714 -194.779 < 2e-16 ***
DESTIN_SZTPSZ08 -1.5629751 0.0091068 -171.627 < 2e-16 ***
DESTIN_SZTPSZ09 -0.5213204 0.0067798 -76.894 < 2e-16 ***
DESTIN_SZTPSZ10 -1.5405668 0.0088453 -174.167 < 2e-16 ***
DESTIN_SZTPSZ11 -0.3590295 0.0053503 -67.104 < 2e-16 ***
DESTIN_SZTPSZ12 -0.8471914 0.0064016 -132.340 < 2e-16 ***
DESTIN_SZTSSZ01 0.3601972 0.0209066 17.229 < 2e-16 ***
DESTIN_SZTSSZ02 1.1511920 0.0133733 86.081 < 2e-16 ***
DESTIN_SZTSSZ03 2.2050639 0.0076710 287.455 < 2e-16 ***
DESTIN_SZTSSZ04 1.9483194 0.0080326 242.552 < 2e-16 ***
DESTIN_SZTSSZ05 2.9897329 0.0075194 397.604 < 2e-16 ***
DESTIN_SZTSSZ06 3.5293877 0.0141456 249.505 < 2e-16 ***
DESTIN_SZWCSZ01 2.9055772 0.0046449 625.542 < 2e-16 ***
DESTIN_SZWCSZ02 -0.9587249 0.0123688 -77.511 < 2e-16 ***
DESTIN_SZWCSZ03 -1.8482203 0.0325154 -56.841 < 2e-16 ***
DESTIN_SZWDSZ01 1.4828743 0.0035172 421.604 < 2e-16 ***
DESTIN_SZWDSZ02 -0.1326910 0.0059446 -22.321 < 2e-16 ***
DESTIN_SZWDSZ03 0.9057458 0.0045064 200.992 < 2e-16 ***
DESTIN_SZWDSZ04 0.0501618 0.0067616 7.419 1.18e-13 ***
DESTIN_SZWDSZ05 0.0859426 0.0066889 12.849 < 2e-16 ***
DESTIN_SZWDSZ06 0.7726353 0.0045597 169.450 < 2e-16 ***
DESTIN_SZWDSZ07 -0.1381768 0.0063899 -21.624 < 2e-16 ***
DESTIN_SZWDSZ08 0.2734527 0.0062547 43.719 < 2e-16 ***
DESTIN_SZWDSZ09 1.2089199 0.0046579 259.539 < 2e-16 ***
DESTIN_SZYSSZ01 0.8509929 0.0038910 218.706 < 2e-16 ***
DESTIN_SZYSSZ02 0.3372571 0.0051028 66.093 < 2e-16 ***
DESTIN_SZYSSZ03 -0.0594889 0.0061746 -9.635 < 2e-16 ***
DESTIN_SZYSSZ04 0.0470398 0.0052771 8.914 < 2e-16 ***
DESTIN_SZYSSZ05 -0.9994384 0.0108536 -92.084 < 2e-16 ***
DESTIN_SZYSSZ06 -1.2678426 0.0106183 -119.402 < 2e-16 ***
DESTIN_SZYSSZ07 -0.6526080 0.0142273 -45.870 < 2e-16 ***
DESTIN_SZYSSZ08 1.0506169 0.0040056 262.287 < 2e-16 ***
DESTIN_SZYSSZ09 0.4584003 0.0042185 108.663 < 2e-16 ***
log(ORIGIN_AGE25_64) 0.2043532 0.0001495 1367.295 < 2e-16 ***
log(dist) -1.7458136 0.0004145 -4212.137 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 47094011 on 14470 degrees of freedom
Residual deviance: 15963058 on 14189 degrees of freedom
AIC: 16052761
Number of Fisher Scoring iterations: 7Let’s check the R-square values of destination constrained SIM model this time.
CalcRSquared(decSIM$data$TRIPS, decSIM$fitted.values)[1] 0.5123583It’s interesting to see that R-squared improves than origin constrained model.
9.6 Doubly Constrained Spatial Interaction Model
In this section, we will calibrate a doubly constrained SIM. For doubly constrained SIM, both the attractiveness at the destinations and the propulsiveness at the origins are considered. The model is typically expressed in the form of a distance function between the origin and destination.
dbcSIM <- glm(formula = TRIPS ~
ORIGIN_SZ +
DESTIN_SZ +
log(dist),
family = poisson(link = "log"),
data = SIM_data,
na.action = na.exclude)
summary(dbcSIM)
Call:
glm(formula = TRIPS ~ ORIGIN_SZ + DESTIN_SZ + log(dist), family = poisson(link = "log"),
data = SIM_data, na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 21.8312374 0.0059160 3690.190 < 2e-16 ***
ORIGIN_SZAMSZ02 0.5263502 0.0048031 109.585 < 2e-16 ***
ORIGIN_SZAMSZ03 0.3139982 0.0049254 63.751 < 2e-16 ***
ORIGIN_SZAMSZ04 -0.2146257 0.0053639 -40.013 < 2e-16 ***
ORIGIN_SZAMSZ05 -0.1890446 0.0060386 -31.306 < 2e-16 ***
ORIGIN_SZAMSZ06 0.1539201 0.0054401 28.294 < 2e-16 ***
ORIGIN_SZAMSZ07 -0.9826565 0.0098676 -99.584 < 2e-16 ***
ORIGIN_SZAMSZ08 -0.4488417 0.0093070 -48.226 < 2e-16 ***
ORIGIN_SZAMSZ09 0.0713474 0.0057402 12.429 < 2e-16 ***
ORIGIN_SZAMSZ10 0.4313742 0.0050370 85.641 < 2e-16 ***
ORIGIN_SZAMSZ11 -1.4712226 0.0131178 -112.154 < 2e-16 ***
ORIGIN_SZAMSZ12 -1.7250733 0.0111603 -154.573 < 2e-16 ***
ORIGIN_SZBDSZ01 0.8810576 0.0048168 182.914 < 2e-16 ***
ORIGIN_SZBDSZ02 0.1100240 0.0055529 19.814 < 2e-16 ***
ORIGIN_SZBDSZ03 0.3606166 0.0050672 71.167 < 2e-16 ***
ORIGIN_SZBDSZ04 1.4624347 0.0044212 330.781 < 2e-16 ***
ORIGIN_SZBDSZ05 0.6207557 0.0050843 122.092 < 2e-16 ***
ORIGIN_SZBDSZ06 0.6712973 0.0051953 129.214 < 2e-16 ***
ORIGIN_SZBDSZ07 -1.2338669 0.0100775 -122.437 < 2e-16 ***
ORIGIN_SZBDSZ08 -1.0444562 0.0094555 -110.460 < 2e-16 ***
ORIGIN_SZBKSZ01 -0.2838426 0.0071354 -39.780 < 2e-16 ***
ORIGIN_SZBKSZ02 0.5550522 0.0059014 94.054 < 2e-16 ***
ORIGIN_SZBKSZ03 0.7396640 0.0056796 130.231 < 2e-16 ***
ORIGIN_SZBKSZ04 -0.2242451 0.0067482 -33.230 < 2e-16 ***
ORIGIN_SZBKSZ05 -0.2371614 0.0069386 -34.180 < 2e-16 ***
ORIGIN_SZBKSZ06 -0.1413812 0.0065035 -21.739 < 2e-16 ***
ORIGIN_SZBKSZ07 0.7089989 0.0051843 136.758 < 2e-16 ***
ORIGIN_SZBKSZ08 -0.0907065 0.0059157 -15.333 < 2e-16 ***
ORIGIN_SZBKSZ09 -0.1775146 0.0063302 -28.042 < 2e-16 ***
ORIGIN_SZBLSZ01 -2.3684539 0.0154280 -153.516 < 2e-16 ***
ORIGIN_SZBLSZ02 -2.8078475 0.0197839 -141.926 < 2e-16 ***
ORIGIN_SZBLSZ03 -3.3122763 0.0466091 -71.065 < 2e-16 ***
ORIGIN_SZBLSZ04 -2.6770542 0.0241793 -110.717 < 2e-16 ***
ORIGIN_SZBMSZ01 0.0618035 0.0059400 10.405 < 2e-16 ***
ORIGIN_SZBMSZ02 -1.3535767 0.0073741 -183.557 < 2e-16 ***
ORIGIN_SZBMSZ03 -0.7569095 0.0063187 -119.790 < 2e-16 ***
ORIGIN_SZBMSZ04 -0.2949304 0.0059603 -49.483 < 2e-16 ***
ORIGIN_SZBMSZ05 -2.6131992 0.0172376 -151.599 < 2e-16 ***
ORIGIN_SZBMSZ06 -3.0315024 0.0185502 -163.422 < 2e-16 ***
ORIGIN_SZBMSZ07 -0.6962524 0.0064068 -108.674 < 2e-16 ***
ORIGIN_SZBMSZ08 -0.9310730 0.0064541 -144.261 < 2e-16 ***
ORIGIN_SZBMSZ09 -1.2911253 0.0092047 -140.268 < 2e-16 ***
ORIGIN_SZBMSZ10 -1.6687004 0.0095708 -174.353 < 2e-16 ***
ORIGIN_SZBMSZ11 -1.1152794 0.0072027 -154.841 < 2e-16 ***
ORIGIN_SZBMSZ12 -1.5323954 0.0099932 -153.344 < 2e-16 ***
ORIGIN_SZBMSZ13 -0.6267376 0.0065863 -95.158 < 2e-16 ***
ORIGIN_SZBMSZ14 -1.0475467 0.0072472 -144.544 < 2e-16 ***
ORIGIN_SZBMSZ15 -0.5049444 0.0067390 -74.929 < 2e-16 ***
ORIGIN_SZBMSZ16 -1.5282897 0.0099545 -153.527 < 2e-16 ***
ORIGIN_SZBMSZ17 -1.5722349 0.0161533 -97.332 < 2e-16 ***
ORIGIN_SZBPSZ01 0.5814175 0.0062904 92.429 < 2e-16 ***
ORIGIN_SZBPSZ02 0.0875442 0.0072190 12.127 < 2e-16 ***
ORIGIN_SZBPSZ03 0.3358227 0.0070460 47.662 < 2e-16 ***
ORIGIN_SZBPSZ04 0.6507586 0.0057726 112.733 < 2e-16 ***
ORIGIN_SZBPSZ05 0.9502124 0.0052971 179.384 < 2e-16 ***
ORIGIN_SZBPSZ06 -1.0480314 0.0098191 -106.734 < 2e-16 ***
ORIGIN_SZBPSZ07 -0.5467931 0.0091676 -59.644 < 2e-16 ***
ORIGIN_SZBSSZ01 0.2998334 0.0059193 50.654 < 2e-16 ***
ORIGIN_SZBSSZ02 0.2841036 0.0050863 55.856 < 2e-16 ***
ORIGIN_SZBSSZ03 -0.2331505 0.0056565 -41.218 < 2e-16 ***
ORIGIN_SZBTSZ01 0.0987284 0.0063715 15.495 < 2e-16 ***
ORIGIN_SZBTSZ02 -0.6261229 0.0084604 -74.006 < 2e-16 ***
ORIGIN_SZBTSZ03 -0.4326963 0.0073452 -58.909 < 2e-16 ***
ORIGIN_SZBTSZ04 -1.4998668 0.0110013 -136.336 < 2e-16 ***
ORIGIN_SZBTSZ05 -0.9564768 0.0122202 -78.270 < 2e-16 ***
ORIGIN_SZBTSZ06 -1.2853131 0.0099328 -129.401 < 2e-16 ***
ORIGIN_SZBTSZ07 -2.3870991 0.0144589 -165.096 < 2e-16 ***
ORIGIN_SZBTSZ08 -1.3715855 0.0113825 -120.499 < 2e-16 ***
ORIGIN_SZCBSZ01 -3.5940232 0.0548979 -65.467 < 2e-16 ***
ORIGIN_SZCCSZ01 -0.7008220 0.0140373 -49.926 < 2e-16 ***
ORIGIN_SZCHSZ01 -0.9109524 0.0122869 -74.140 < 2e-16 ***
ORIGIN_SZCHSZ02 -0.8566547 0.0088749 -96.526 < 2e-16 ***
ORIGIN_SZCHSZ03 1.1153731 0.0066136 168.650 < 2e-16 ***
ORIGIN_SZCKSZ01 0.3001815 0.0058548 51.271 < 2e-16 ***
ORIGIN_SZCKSZ02 0.7185711 0.0060595 118.585 < 2e-16 ***
ORIGIN_SZCKSZ03 1.1389824 0.0053179 214.178 < 2e-16 ***
ORIGIN_SZCKSZ04 1.6281772 0.0054761 297.324 < 2e-16 ***
ORIGIN_SZCKSZ05 0.8338470 0.0064178 129.927 < 2e-16 ***
ORIGIN_SZCKSZ06 0.6528993 0.0082375 79.259 < 2e-16 ***
ORIGIN_SZCLSZ01 -0.7174758 0.0082123 -87.366 < 2e-16 ***
ORIGIN_SZCLSZ02 -1.7513100 0.0139062 -125.938 < 2e-16 ***
ORIGIN_SZCLSZ03 -1.0362873 0.0085485 -121.224 < 2e-16 ***
ORIGIN_SZCLSZ04 0.6160017 0.0051276 120.136 < 2e-16 ***
ORIGIN_SZCLSZ05 -2.1005122 0.0150228 -139.821 < 2e-16 ***
ORIGIN_SZCLSZ06 0.7252108 0.0049447 146.665 < 2e-16 ***
ORIGIN_SZCLSZ07 -0.5343482 0.0062500 -85.496 < 2e-16 ***
ORIGIN_SZCLSZ08 -0.2153408 0.0067571 -31.869 < 2e-16 ***
ORIGIN_SZCLSZ09 -1.8019961 0.0169078 -106.578 < 2e-16 ***
ORIGIN_SZDTSZ02 -3.9057711 0.0834668 -46.794 < 2e-16 ***
ORIGIN_SZDTSZ03 -3.4152419 0.0738650 -46.236 < 2e-16 ***
ORIGIN_SZDTSZ13 -3.0183438 0.0315257 -95.742 < 2e-16 ***
ORIGIN_SZGLSZ01 -1.7812384 0.0099367 -179.258 < 2e-16 ***
ORIGIN_SZGLSZ02 -0.1074991 0.0054325 -19.788 < 2e-16 ***
ORIGIN_SZGLSZ03 -0.2461106 0.0057176 -43.045 < 2e-16 ***
ORIGIN_SZGLSZ04 0.8657186 0.0046413 186.524 < 2e-16 ***
ORIGIN_SZGLSZ05 0.5871393 0.0047939 122.477 < 2e-16 ***
ORIGIN_SZHGSZ01 0.3543819 0.0050461 70.229 < 2e-16 ***
ORIGIN_SZHGSZ02 0.4218178 0.0050820 83.003 < 2e-16 ***
ORIGIN_SZHGSZ03 0.2411309 0.0054241 44.456 < 2e-16 ***
ORIGIN_SZHGSZ04 0.8180622 0.0046153 177.252 < 2e-16 ***
ORIGIN_SZHGSZ05 1.2173687 0.0045655 266.647 < 2e-16 ***
ORIGIN_SZHGSZ06 -0.1826300 0.0058214 -31.372 < 2e-16 ***
ORIGIN_SZHGSZ07 0.3172839 0.0050733 62.540 < 2e-16 ***
ORIGIN_SZHGSZ08 -0.1151369 0.0057067 -20.176 < 2e-16 ***
ORIGIN_SZHGSZ09 -1.2873441 0.0091690 -140.401 < 2e-16 ***
ORIGIN_SZHGSZ10 -3.3783178 0.0424682 -79.549 < 2e-16 ***
ORIGIN_SZJESZ01 0.4859234 0.0055927 86.885 < 2e-16 ***
ORIGIN_SZJESZ02 0.1766088 0.0055800 31.650 < 2e-16 ***
ORIGIN_SZJESZ03 -0.2177441 0.0059535 -36.574 < 2e-16 ***
ORIGIN_SZJESZ04 -1.5532182 0.0104526 -148.597 < 2e-16 ***
ORIGIN_SZJESZ05 -2.3332926 0.0142701 -163.509 < 2e-16 ***
ORIGIN_SZJESZ06 0.3007382 0.0055019 54.661 < 2e-16 ***
ORIGIN_SZJESZ07 -1.9687994 0.0121092 -162.587 < 2e-16 ***
ORIGIN_SZJESZ08 -1.3032070 0.0122024 -106.800 < 2e-16 ***
ORIGIN_SZJESZ09 0.5762635 0.0058766 98.061 < 2e-16 ***
ORIGIN_SZJESZ10 -1.4423113 0.0194773 -74.051 < 2e-16 ***
ORIGIN_SZJESZ11 -1.9720897 0.0200811 -98.206 < 2e-16 ***
ORIGIN_SZJWSZ01 0.3808627 0.0071357 53.374 < 2e-16 ***
ORIGIN_SZJWSZ02 0.7963999 0.0053150 149.840 < 2e-16 ***
ORIGIN_SZJWSZ03 1.5429636 0.0049961 308.834 < 2e-16 ***
ORIGIN_SZJWSZ04 0.6410760 0.0056711 113.042 < 2e-16 ***
ORIGIN_SZJWSZ05 -2.1571049 0.0133584 -161.479 < 2e-16 ***
ORIGIN_SZJWSZ06 -1.5174532 0.0113384 -133.833 < 2e-16 ***
ORIGIN_SZJWSZ07 -2.7089963 0.0280439 -96.598 < 2e-16 ***
ORIGIN_SZJWSZ08 1.5343415 0.0051711 296.713 < 2e-16 ***
ORIGIN_SZJWSZ09 1.8837410 0.0048845 385.656 < 2e-16 ***
ORIGIN_SZKLSZ01 0.1081286 0.0053307 20.284 < 2e-16 ***
ORIGIN_SZKLSZ02 -0.8844695 0.0067728 -130.591 < 2e-16 ***
ORIGIN_SZKLSZ03 -0.6872640 0.0062857 -109.337 < 2e-16 ***
ORIGIN_SZKLSZ04 -2.2090319 0.0122440 -180.418 < 2e-16 ***
ORIGIN_SZKLSZ05 -1.1728726 0.0110765 -105.888 < 2e-16 ***
ORIGIN_SZKLSZ06 -6.1162315 0.1857789 -32.922 < 2e-16 ***
ORIGIN_SZKLSZ07 -1.4082749 0.0092299 -152.578 < 2e-16 ***
ORIGIN_SZKLSZ08 -1.7781551 0.0104682 -169.862 < 2e-16 ***
ORIGIN_SZLKSZ01 -2.0531568 0.0398803 -51.483 < 2e-16 ***
ORIGIN_SZMDSZ01 -0.8825639 0.0287621 -30.685 < 2e-16 ***
ORIGIN_SZMDSZ02 -0.6219993 0.0107388 -57.921 < 2e-16 ***
ORIGIN_SZMDSZ03 -2.0840156 0.0173117 -120.382 < 2e-16 ***
ORIGIN_SZMPSZ01 -0.9659093 0.0086972 -111.060 < 2e-16 ***
ORIGIN_SZMPSZ02 -1.0411153 0.0073403 -141.836 < 2e-16 ***
ORIGIN_SZMPSZ03 0.0001659 0.0059401 0.028 0.977719
ORIGIN_SZMUSZ02 -3.7599031 0.1037937 -36.225 < 2e-16 ***
ORIGIN_SZNTSZ01 -3.0388366 0.0355325 -85.523 < 2e-16 ***
ORIGIN_SZNTSZ02 -3.4230640 0.0235902 -145.106 < 2e-16 ***
ORIGIN_SZNTSZ03 -0.9094796 0.0082551 -110.172 < 2e-16 ***
ORIGIN_SZNTSZ05 -4.0861681 0.0499630 -81.784 < 2e-16 ***
ORIGIN_SZNTSZ06 -3.9497128 0.0565388 -69.858 < 2e-16 ***
ORIGIN_SZNVSZ01 0.3235636 0.0049439 65.447 < 2e-16 ***
ORIGIN_SZNVSZ02 -0.6946748 0.0070536 -98.485 < 2e-16 ***
ORIGIN_SZNVSZ03 -1.0540196 0.0083781 -125.806 < 2e-16 ***
ORIGIN_SZNVSZ04 -0.9897977 0.0093463 -105.903 < 2e-16 ***
ORIGIN_SZNVSZ05 -2.2578432 0.0169180 -133.458 < 2e-16 ***
ORIGIN_SZPGSZ01 0.2399827 0.0130436 18.398 < 2e-16 ***
ORIGIN_SZPGSZ02 -0.3352342 0.0078451 -42.732 < 2e-16 ***
ORIGIN_SZPGSZ03 0.9515148 0.0051376 185.207 < 2e-16 ***
ORIGIN_SZPGSZ04 1.3998952 0.0047991 291.697 < 2e-16 ***
ORIGIN_SZPGSZ05 0.4451629 0.0063423 70.189 < 2e-16 ***
ORIGIN_SZPLSZ01 -0.9705918 0.0122781 -79.050 < 2e-16 ***
ORIGIN_SZPLSZ02 -1.0670151 0.0153358 -69.577 < 2e-16 ***
ORIGIN_SZPLSZ03 -2.1229124 0.0373527 -56.834 < 2e-16 ***
ORIGIN_SZPLSZ04 -3.0911932 0.0371296 -83.254 < 2e-16 ***
ORIGIN_SZPLSZ05 -2.1705708 0.0226085 -96.007 < 2e-16 ***
ORIGIN_SZPNSZ01 0.9052637 0.0065952 137.262 < 2e-16 ***
ORIGIN_SZPNSZ02 -0.1720425 0.0125658 -13.691 < 2e-16 ***
ORIGIN_SZPNSZ03 -2.3973459 0.0201408 -119.029 < 2e-16 ***
ORIGIN_SZPNSZ04 -3.4483689 0.0343741 -100.319 < 2e-16 ***
ORIGIN_SZPNSZ05 -2.0588530 0.0282328 -72.924 < 2e-16 ***
ORIGIN_SZPRSZ01 -0.6399015 0.0120470 -53.117 < 2e-16 ***
ORIGIN_SZPRSZ02 0.8122270 0.0050886 159.617 < 2e-16 ***
ORIGIN_SZPRSZ03 0.3990960 0.0051810 77.031 < 2e-16 ***
ORIGIN_SZPRSZ04 -0.8485348 0.0079236 -107.089 < 2e-16 ***
ORIGIN_SZPRSZ05 0.8008791 0.0048532 165.021 < 2e-16 ***
ORIGIN_SZPRSZ06 -1.4498806 0.0121422 -119.408 < 2e-16 ***
ORIGIN_SZPRSZ07 -3.2025045 0.0167118 -191.631 < 2e-16 ***
ORIGIN_SZPRSZ08 -0.5862269 0.0067255 -87.165 < 2e-16 ***
ORIGIN_SZQTSZ01 -0.1859270 0.0075531 -24.616 < 2e-16 ***
ORIGIN_SZQTSZ02 -0.8715122 0.0068124 -127.929 < 2e-16 ***
ORIGIN_SZQTSZ03 -0.1259816 0.0064796 -19.443 < 2e-16 ***
ORIGIN_SZQTSZ04 -1.4620032 0.0079848 -183.098 < 2e-16 ***
ORIGIN_SZQTSZ05 -0.6675643 0.0069616 -95.892 < 2e-16 ***
ORIGIN_SZQTSZ06 -0.8190026 0.0072713 -112.634 < 2e-16 ***
ORIGIN_SZQTSZ07 -1.5189403 0.0099864 -152.101 < 2e-16 ***
ORIGIN_SZQTSZ08 -0.4976238 0.0067874 -73.316 < 2e-16 ***
ORIGIN_SZQTSZ09 -0.9006162 0.0075978 -118.536 < 2e-16 ***
ORIGIN_SZQTSZ10 -0.6690184 0.0071574 -93.473 < 2e-16 ***
ORIGIN_SZQTSZ11 -2.5203437 0.0147000 -171.452 < 2e-16 ***
ORIGIN_SZQTSZ12 -3.0461675 0.0190193 -160.162 < 2e-16 ***
ORIGIN_SZQTSZ13 -0.7501068 0.0084481 -88.791 < 2e-16 ***
ORIGIN_SZQTSZ14 -1.9321849 0.0126114 -153.209 < 2e-16 ***
ORIGIN_SZQTSZ15 -0.9576828 0.0127157 -75.315 < 2e-16 ***
ORIGIN_SZRCSZ01 -1.8167951 0.0129234 -140.582 < 2e-16 ***
ORIGIN_SZRCSZ06 -0.5560563 0.0090507 -61.438 < 2e-16 ***
ORIGIN_SZRVSZ01 -2.8862570 0.0325532 -88.663 < 2e-16 ***
ORIGIN_SZRVSZ02 -3.1555662 0.0281279 -112.186 < 2e-16 ***
ORIGIN_SZRVSZ03 -2.9836089 0.0248449 -120.089 < 2e-16 ***
ORIGIN_SZRVSZ04 -3.5520422 0.0561371 -63.274 < 2e-16 ***
ORIGIN_SZRVSZ05 -2.5866584 0.0180382 -143.399 < 2e-16 ***
ORIGIN_SZSBSZ01 0.2867444 0.0071098 40.331 < 2e-16 ***
ORIGIN_SZSBSZ02 -0.9012334 0.0087262 -103.278 < 2e-16 ***
ORIGIN_SZSBSZ03 0.8311038 0.0055422 149.958 < 2e-16 ***
ORIGIN_SZSBSZ04 0.4044170 0.0062047 65.179 < 2e-16 ***
ORIGIN_SZSBSZ05 -0.2661845 0.0074162 -35.892 < 2e-16 ***
ORIGIN_SZSBSZ06 -0.9023075 0.0175046 -51.547 < 2e-16 ***
ORIGIN_SZSBSZ07 0.0505870 0.0131317 3.852 0.000117 ***
ORIGIN_SZSBSZ08 -1.1158011 0.0145416 -76.732 < 2e-16 ***
ORIGIN_SZSBSZ09 -0.9682835 0.0095396 -101.501 < 2e-16 ***
ORIGIN_SZSESZ02 1.1452735 0.0047810 239.548 < 2e-16 ***
ORIGIN_SZSESZ03 1.2815277 0.0045677 280.564 < 2e-16 ***
ORIGIN_SZSESZ04 0.8085857 0.0052756 153.269 < 2e-16 ***
ORIGIN_SZSESZ05 -0.2329413 0.0063113 -36.909 < 2e-16 ***
ORIGIN_SZSESZ06 1.0576879 0.0049909 211.925 < 2e-16 ***
ORIGIN_SZSESZ07 -2.3165908 0.0196831 -117.695 < 2e-16 ***
ORIGIN_SZSGSZ01 -0.6606350 0.0088079 -75.005 < 2e-16 ***
ORIGIN_SZSGSZ02 -1.3638984 0.0104040 -131.094 < 2e-16 ***
ORIGIN_SZSGSZ03 0.1152591 0.0054649 21.091 < 2e-16 ***
ORIGIN_SZSGSZ04 0.2954067 0.0050865 58.077 < 2e-16 ***
ORIGIN_SZSGSZ05 -2.0792678 0.0109882 -189.227 < 2e-16 ***
ORIGIN_SZSGSZ06 0.4563227 0.0048880 93.356 < 2e-16 ***
ORIGIN_SZSGSZ07 -0.8955254 0.0067100 -133.461 < 2e-16 ***
ORIGIN_SZSKSZ01 -0.3184402 0.0093032 -34.229 < 2e-16 ***
ORIGIN_SZSKSZ02 1.1160484 0.0063851 174.790 < 2e-16 ***
ORIGIN_SZSKSZ03 -0.2566692 0.0086021 -29.838 < 2e-16 ***
ORIGIN_SZSKSZ04 -1.5781827 0.0279394 -56.486 < 2e-16 ***
ORIGIN_SZSKSZ05 -0.2724361 0.0163597 -16.653 < 2e-16 ***
ORIGIN_SZSLSZ01 -2.4458625 0.0330301 -74.050 < 2e-16 ***
ORIGIN_SZSLSZ04 -0.0987076 0.0079626 -12.396 < 2e-16 ***
ORIGIN_SZSRSZ01 -2.2584977 0.0176647 -127.854 < 2e-16 ***
ORIGIN_SZTHSZ01 -2.5878524 0.0489998 -52.814 < 2e-16 ***
ORIGIN_SZTHSZ03 -0.8101746 0.0226814 -35.720 < 2e-16 ***
ORIGIN_SZTHSZ04 -2.4186655 0.0288663 -83.789 < 2e-16 ***
ORIGIN_SZTHSZ06 -1.7080541 0.0186353 -91.657 < 2e-16 ***
ORIGIN_SZTMSZ01 -0.2193476 0.0061823 -35.480 < 2e-16 ***
ORIGIN_SZTMSZ02 1.7772464 0.0043394 409.558 < 2e-16 ***
ORIGIN_SZTMSZ03 1.0051343 0.0046055 218.249 < 2e-16 ***
ORIGIN_SZTMSZ04 0.1642370 0.0055078 29.819 < 2e-16 ***
ORIGIN_SZTMSZ05 -1.2878706 0.0114828 -112.157 < 2e-16 ***
ORIGIN_SZTNSZ01 -1.7163504 0.0131268 -130.751 < 2e-16 ***
ORIGIN_SZTNSZ02 -1.6508988 0.0103851 -158.968 < 2e-16 ***
ORIGIN_SZTNSZ03 -2.1545577 0.0137947 -156.187 < 2e-16 ***
ORIGIN_SZTNSZ04 -0.3949120 0.0078496 -50.310 < 2e-16 ***
ORIGIN_SZTPSZ01 -0.8058100 0.0069916 -115.253 < 2e-16 ***
ORIGIN_SZTPSZ02 0.5369060 0.0047272 113.577 < 2e-16 ***
ORIGIN_SZTPSZ03 -0.7779333 0.0064278 -121.027 < 2e-16 ***
ORIGIN_SZTPSZ04 -0.8153581 0.0061387 -132.823 < 2e-16 ***
ORIGIN_SZTPSZ05 -0.5073676 0.0067771 -74.865 < 2e-16 ***
ORIGIN_SZTPSZ06 0.0847301 0.0065717 12.893 < 2e-16 ***
ORIGIN_SZTPSZ07 -0.5839519 0.0066148 -88.280 < 2e-16 ***
ORIGIN_SZTPSZ08 -1.0577941 0.0098480 -107.412 < 2e-16 ***
ORIGIN_SZTPSZ09 -0.9067707 0.0071367 -127.057 < 2e-16 ***
ORIGIN_SZTPSZ10 -1.1362091 0.0080905 -140.438 < 2e-16 ***
ORIGIN_SZTPSZ11 -0.2374621 0.0059472 -39.928 < 2e-16 ***
ORIGIN_SZTPSZ12 -0.8028874 0.0069663 -115.253 < 2e-16 ***
ORIGIN_SZTSSZ01 -2.7809271 0.0482843 -57.595 < 2e-16 ***
ORIGIN_SZTSSZ02 0.0425804 0.0105088 4.052 5.08e-05 ***
ORIGIN_SZTSSZ03 0.1142369 0.0109412 10.441 < 2e-16 ***
ORIGIN_SZTSSZ04 -0.6186261 0.0116324 -53.181 < 2e-16 ***
ORIGIN_SZTSSZ05 -1.0846732 0.0173555 -62.497 < 2e-16 ***
ORIGIN_SZTSSZ06 0.3980173 0.0198100 20.092 < 2e-16 ***
ORIGIN_SZWCSZ01 1.3545143 0.0092002 147.227 < 2e-16 ***
ORIGIN_SZWCSZ02 -2.9863278 0.0330906 -90.247 < 2e-16 ***
ORIGIN_SZWCSZ03 -5.0504916 0.1241385 -40.684 < 2e-16 ***
ORIGIN_SZWDSZ01 1.5238429 0.0049404 308.448 < 2e-16 ***
ORIGIN_SZWDSZ02 0.2832576 0.0056218 50.386 < 2e-16 ***
ORIGIN_SZWDSZ03 1.3702524 0.0053266 257.245 < 2e-16 ***
ORIGIN_SZWDSZ04 1.0248225 0.0059272 172.903 < 2e-16 ***
ORIGIN_SZWDSZ05 0.2356778 0.0060587 38.899 < 2e-16 ***
ORIGIN_SZWDSZ06 0.3146925 0.0059919 52.520 < 2e-16 ***
ORIGIN_SZWDSZ07 -1.4971897 0.0091243 -164.088 < 2e-16 ***
ORIGIN_SZWDSZ08 -0.8894079 0.0087414 -101.747 < 2e-16 ***
ORIGIN_SZWDSZ09 1.4437633 0.0053160 271.590 < 2e-16 ***
ORIGIN_SZYSSZ01 -0.2519398 0.0064443 -39.095 < 2e-16 ***
ORIGIN_SZYSSZ02 0.8726785 0.0057658 151.354 < 2e-16 ***
ORIGIN_SZYSSZ03 1.7868139 0.0050674 352.611 < 2e-16 ***
ORIGIN_SZYSSZ04 0.8418040 0.0051738 162.704 < 2e-16 ***
ORIGIN_SZYSSZ05 0.4292096 0.0062520 68.652 < 2e-16 ***
ORIGIN_SZYSSZ06 -0.7459961 0.0119123 -62.624 < 2e-16 ***
ORIGIN_SZYSSZ07 -0.8422281 0.0144559 -58.262 < 2e-16 ***
ORIGIN_SZYSSZ08 0.1829428 0.0067885 26.949 < 2e-16 ***
ORIGIN_SZYSSZ09 1.1159712 0.0050760 219.853 < 2e-16 ***
DESTIN_SZAMSZ02 0.0694567 0.0045966 15.111 < 2e-16 ***
DESTIN_SZAMSZ03 0.0760100 0.0044639 17.028 < 2e-16 ***
DESTIN_SZAMSZ04 -1.1306391 0.0064373 -175.639 < 2e-16 ***
DESTIN_SZAMSZ05 -1.0751133 0.0065164 -164.985 < 2e-16 ***
DESTIN_SZAMSZ06 -0.9624298 0.0065937 -145.962 < 2e-16 ***
DESTIN_SZAMSZ07 -1.5060319 0.0097616 -154.281 < 2e-16 ***
DESTIN_SZAMSZ08 -0.4813202 0.0069794 -68.963 < 2e-16 ***
DESTIN_SZAMSZ09 -1.0220675 0.0066313 -154.129 < 2e-16 ***
DESTIN_SZAMSZ10 0.1235142 0.0047044 26.255 < 2e-16 ***
DESTIN_SZAMSZ11 -0.8917993 0.0088519 -100.746 < 2e-16 ***
DESTIN_SZAMSZ12 0.0195208 0.0051704 3.775 0.000160 ***
DESTIN_SZBDSZ01 0.9736349 0.0042757 227.713 < 2e-16 ***
DESTIN_SZBDSZ02 -0.1969470 0.0055284 -35.625 < 2e-16 ***
DESTIN_SZBDSZ03 0.1266471 0.0050786 24.938 < 2e-16 ***
DESTIN_SZBDSZ04 1.1608485 0.0041956 276.684 < 2e-16 ***
DESTIN_SZBDSZ05 0.9293840 0.0044412 209.265 < 2e-16 ***
DESTIN_SZBDSZ06 0.4090567 0.0050300 81.323 < 2e-16 ***
DESTIN_SZBDSZ07 -0.8171478 0.0098945 -82.586 < 2e-16 ***
DESTIN_SZBDSZ08 -1.5895287 0.0111632 -142.391 < 2e-16 ***
DESTIN_SZBKSZ01 -1.3793311 0.0072145 -191.189 < 2e-16 ***
DESTIN_SZBKSZ02 -0.5253670 0.0061879 -84.903 < 2e-16 ***
DESTIN_SZBKSZ03 -1.0095362 0.0065426 -154.301 < 2e-16 ***
DESTIN_SZBKSZ04 -0.5662858 0.0056453 -100.311 < 2e-16 ***
DESTIN_SZBKSZ05 -0.9406607 0.0070597 -133.244 < 2e-16 ***
DESTIN_SZBKSZ06 -1.3129276 0.0067414 -194.755 < 2e-16 ***
DESTIN_SZBKSZ07 0.0120605 0.0049284 2.447 0.014400 *
DESTIN_SZBKSZ08 -1.3658471 0.0075109 -181.849 < 2e-16 ***
DESTIN_SZBKSZ09 -0.1771310 0.0055645 -31.832 < 2e-16 ***
DESTIN_SZBLSZ01 -0.8175223 0.0075645 -108.074 < 2e-16 ***
DESTIN_SZBLSZ02 0.1631280 0.0071753 22.735 < 2e-16 ***
DESTIN_SZBLSZ03 1.2598494 0.0081706 154.194 < 2e-16 ***
DESTIN_SZBLSZ04 -0.5642975 0.0137827 -40.943 < 2e-16 ***
DESTIN_SZBMSZ01 0.6921844 0.0054211 127.684 < 2e-16 ***
DESTIN_SZBMSZ02 -0.1209392 0.0055362 -21.845 < 2e-16 ***
DESTIN_SZBMSZ03 -0.2373881 0.0062427 -38.027 < 2e-16 ***
DESTIN_SZBMSZ04 -0.0407117 0.0058001 -7.019 2.23e-12 ***
DESTIN_SZBMSZ05 -0.2363309 0.0075967 -31.110 < 2e-16 ***
DESTIN_SZBMSZ06 -1.1930710 0.0134761 -88.532 < 2e-16 ***
DESTIN_SZBMSZ07 0.4625103 0.0051864 89.178 < 2e-16 ***
DESTIN_SZBMSZ08 -0.8604731 0.0069899 -123.102 < 2e-16 ***
DESTIN_SZBMSZ09 -2.1290239 0.0154841 -137.498 < 2e-16 ***
DESTIN_SZBMSZ10 -1.4617153 0.0094014 -155.478 < 2e-16 ***
DESTIN_SZBMSZ11 -1.3234050 0.0085506 -154.773 < 2e-16 ***
DESTIN_SZBMSZ12 -0.8399230 0.0085361 -98.397 < 2e-16 ***
DESTIN_SZBMSZ13 0.1366529 0.0059697 22.891 < 2e-16 ***
DESTIN_SZBMSZ14 -1.0491968 0.0083021 -126.378 < 2e-16 ***
DESTIN_SZBMSZ15 -0.6726684 0.0076276 -88.189 < 2e-16 ***
DESTIN_SZBMSZ16 -1.4011734 0.0116569 -120.201 < 2e-16 ***
DESTIN_SZBMSZ17 -1.5682752 0.0167333 -93.722 < 2e-16 ***
DESTIN_SZBPSZ01 -1.1120017 0.0063197 -175.959 < 2e-16 ***
DESTIN_SZBPSZ02 -2.0833466 0.0091139 -228.590 < 2e-16 ***
DESTIN_SZBPSZ03 -1.6937265 0.0087437 -193.709 < 2e-16 ***
DESTIN_SZBPSZ04 -0.7964999 0.0066129 -120.447 < 2e-16 ***
DESTIN_SZBPSZ05 0.2109118 0.0048815 43.206 < 2e-16 ***
DESTIN_SZBPSZ06 -1.1808365 0.0083657 -141.152 < 2e-16 ***
DESTIN_SZBPSZ07 -0.2077428 0.0084543 -24.572 < 2e-16 ***
DESTIN_SZBSSZ01 0.3164175 0.0050682 62.431 < 2e-16 ***
DESTIN_SZBSSZ02 -0.4852688 0.0057001 -85.134 < 2e-16 ***
DESTIN_SZBSSZ03 0.4130432 0.0043061 95.921 < 2e-16 ***
DESTIN_SZBTSZ01 0.6215095 0.0048914 127.061 < 2e-16 ***
DESTIN_SZBTSZ02 -0.0145076 0.0071799 -2.021 0.043324 *
DESTIN_SZBTSZ03 0.4919981 0.0058498 84.105 < 2e-16 ***
DESTIN_SZBTSZ04 -0.6957555 0.0114078 -60.989 < 2e-16 ***
DESTIN_SZBTSZ05 0.3329814 0.0073568 45.262 < 2e-16 ***
DESTIN_SZBTSZ06 -0.1333295 0.0073965 -18.026 < 2e-16 ***
DESTIN_SZBTSZ07 -1.4449581 0.0113186 -127.663 < 2e-16 ***
DESTIN_SZBTSZ08 -0.7079056 0.0103797 -68.201 < 2e-16 ***
DESTIN_SZCBSZ01 -5.7344725 0.3162767 -18.131 < 2e-16 ***
DESTIN_SZCCSZ01 -0.0009541 0.0083381 -0.114 0.908900
DESTIN_SZCHSZ01 -0.2083016 0.0099054 -21.029 < 2e-16 ***
DESTIN_SZCHSZ02 0.5369606 0.0057531 93.334 < 2e-16 ***
DESTIN_SZCHSZ03 2.5530638 0.0043945 580.971 < 2e-16 ***
DESTIN_SZCKSZ01 -0.5725975 0.0056507 -101.333 < 2e-16 ***
DESTIN_SZCKSZ02 -1.1181852 0.0063287 -176.685 < 2e-16 ***
DESTIN_SZCKSZ03 0.1156680 0.0049440 23.396 < 2e-16 ***
DESTIN_SZCKSZ04 -0.8647725 0.0071003 -121.794 < 2e-16 ***
DESTIN_SZCKSZ05 -1.1641791 0.0076248 -152.684 < 2e-16 ***
DESTIN_SZCKSZ06 -0.4397612 0.0073040 -60.208 < 2e-16 ***
DESTIN_SZCLSZ01 0.1930552 0.0053752 35.916 < 2e-16 ***
DESTIN_SZCLSZ02 -2.0436501 0.0136039 -150.225 < 2e-16 ***
DESTIN_SZCLSZ03 -0.9338571 0.0082908 -112.638 < 2e-16 ***
DESTIN_SZCLSZ04 0.0532041 0.0053276 9.987 < 2e-16 ***
DESTIN_SZCLSZ05 -1.0782781 0.0088184 -122.276 < 2e-16 ***
DESTIN_SZCLSZ06 0.4068171 0.0049068 82.910 < 2e-16 ***
DESTIN_SZCLSZ07 -0.3579507 0.0060289 -59.373 < 2e-16 ***
DESTIN_SZCLSZ08 -0.2487993 0.0066588 -37.364 < 2e-16 ***
DESTIN_SZCLSZ09 0.1611080 0.0071178 22.635 < 2e-16 ***
DESTIN_SZDTSZ02 -1.7308348 0.0349466 -49.528 < 2e-16 ***
DESTIN_SZDTSZ03 -0.5994253 0.0146230 -40.992 < 2e-16 ***
DESTIN_SZDTSZ13 -1.3685031 0.0162803 -84.059 < 2e-16 ***
DESTIN_SZGLSZ01 -0.0910001 0.0055275 -16.463 < 2e-16 ***
DESTIN_SZGLSZ02 -0.0692224 0.0052840 -13.100 < 2e-16 ***
DESTIN_SZGLSZ03 0.6493421 0.0043446 149.459 < 2e-16 ***
DESTIN_SZGLSZ04 0.9327947 0.0043674 213.583 < 2e-16 ***
DESTIN_SZGLSZ05 0.8161728 0.0043625 187.087 < 2e-16 ***
DESTIN_SZHGSZ01 0.0658625 0.0042516 15.491 < 2e-16 ***
DESTIN_SZHGSZ02 -0.8134329 0.0056721 -143.409 < 2e-16 ***
DESTIN_SZHGSZ03 -1.3546132 0.0066257 -204.448 < 2e-16 ***
DESTIN_SZHGSZ04 -0.4500588 0.0048448 -92.895 < 2e-16 ***
DESTIN_SZHGSZ05 -0.5026431 0.0050996 -98.566 < 2e-16 ***
DESTIN_SZHGSZ06 -0.8673686 0.0059530 -145.704 < 2e-16 ***
DESTIN_SZHGSZ07 0.0560490 0.0047702 11.750 < 2e-16 ***
DESTIN_SZHGSZ08 -0.0443189 0.0052599 -8.426 < 2e-16 ***
DESTIN_SZHGSZ09 -0.0126355 0.0054966 -2.299 0.021518 *
DESTIN_SZHGSZ10 -3.5821793 0.0263281 -136.059 < 2e-16 ***
DESTIN_SZJESZ01 -0.3704281 0.0056684 -65.350 < 2e-16 ***
DESTIN_SZJESZ02 -0.7369159 0.0058686 -125.570 < 2e-16 ***
DESTIN_SZJESZ03 -0.8985484 0.0063627 -141.222 < 2e-16 ***
DESTIN_SZJESZ04 -1.0511995 0.0073996 -142.061 < 2e-16 ***
DESTIN_SZJESZ05 -1.5324974 0.0102612 -149.349 < 2e-16 ***
DESTIN_SZJESZ06 0.3105267 0.0048241 64.370 < 2e-16 ***
DESTIN_SZJESZ07 -1.3234483 0.0085497 -154.795 < 2e-16 ***
DESTIN_SZJESZ08 -0.6559742 0.0083174 -78.867 < 2e-16 ***
DESTIN_SZJESZ09 0.2663752 0.0063370 42.035 < 2e-16 ***
DESTIN_SZJESZ10 0.8529026 0.0076067 112.126 < 2e-16 ***
DESTIN_SZJESZ11 0.5559641 0.0074629 74.497 < 2e-16 ***
DESTIN_SZJWSZ01 -0.9790971 0.0071830 -136.308 < 2e-16 ***
DESTIN_SZJWSZ02 -0.8746590 0.0060179 -145.342 < 2e-16 ***
DESTIN_SZJWSZ03 0.5689062 0.0049105 115.855 < 2e-16 ***
DESTIN_SZJWSZ04 0.4520963 0.0050302 89.876 < 2e-16 ***
DESTIN_SZJWSZ05 -1.0249671 0.0067371 -152.137 < 2e-16 ***
DESTIN_SZJWSZ06 -0.7451483 0.0062189 -119.819 < 2e-16 ***
DESTIN_SZJWSZ07 -2.8453099 0.0287335 -99.024 < 2e-16 ***
DESTIN_SZJWSZ08 -0.3372309 0.0058003 -58.141 < 2e-16 ***
DESTIN_SZJWSZ09 1.0505330 0.0045908 228.832 < 2e-16 ***
DESTIN_SZKLSZ01 -0.2334836 0.0057970 -40.277 < 2e-16 ***
DESTIN_SZKLSZ02 -0.5416148 0.0061432 -88.164 < 2e-16 ***
DESTIN_SZKLSZ03 -0.8026495 0.0068745 -116.757 < 2e-16 ***
DESTIN_SZKLSZ04 -1.2918594 0.0090197 -143.227 < 2e-16 ***
DESTIN_SZKLSZ05 -0.4069101 0.0087812 -46.339 < 2e-16 ***
DESTIN_SZKLSZ06 -2.5333101 0.0363215 -69.747 < 2e-16 ***
DESTIN_SZKLSZ07 -0.6623343 0.0070761 -93.601 < 2e-16 ***
DESTIN_SZKLSZ08 -0.1408205 0.0054965 -25.620 < 2e-16 ***
DESTIN_SZLKSZ01 -1.2639235 0.0208254 -60.691 < 2e-16 ***
DESTIN_SZMDSZ01 -1.5655800 0.0202787 -77.203 < 2e-16 ***
DESTIN_SZMDSZ02 -0.9767682 0.0114687 -85.168 < 2e-16 ***
DESTIN_SZMDSZ03 -3.3328109 0.0254294 -131.061 < 2e-16 ***
DESTIN_SZMPSZ01 -0.4552859 0.0080666 -56.441 < 2e-16 ***
DESTIN_SZMPSZ02 -0.5386560 0.0064620 -83.358 < 2e-16 ***
DESTIN_SZMPSZ03 0.4952000 0.0052295 94.694 < 2e-16 ***
DESTIN_SZMUSZ02 -1.4434175 0.0202509 -71.277 < 2e-16 ***
DESTIN_SZNTSZ01 -2.9194067 0.0449654 -64.926 < 2e-16 ***
DESTIN_SZNTSZ02 -1.3780179 0.0112867 -122.092 < 2e-16 ***
DESTIN_SZNTSZ03 -0.5044699 0.0080449 -62.707 < 2e-16 ***
DESTIN_SZNTSZ05 -2.0017134 0.0258750 -77.361 < 2e-16 ***
DESTIN_SZNTSZ06 -3.8120537 0.0434271 -87.781 < 2e-16 ***
DESTIN_SZNVSZ01 -0.1071506 0.0051026 -20.999 < 2e-16 ***
DESTIN_SZNVSZ02 -0.0274710 0.0057611 -4.768 1.86e-06 ***
DESTIN_SZNVSZ03 0.1076352 0.0057909 18.587 < 2e-16 ***
DESTIN_SZNVSZ04 -1.2087250 0.0110438 -109.448 < 2e-16 ***
DESTIN_SZNVSZ05 -1.0058290 0.0092167 -109.131 < 2e-16 ***
DESTIN_SZPGSZ01 -1.2029931 0.0163170 -73.726 < 2e-16 ***
DESTIN_SZPGSZ02 -1.2878671 0.0074139 -173.709 < 2e-16 ***
DESTIN_SZPGSZ03 -0.1520894 0.0048629 -31.275 < 2e-16 ***
DESTIN_SZPGSZ04 -0.1985959 0.0050374 -39.424 < 2e-16 ***
DESTIN_SZPGSZ05 -1.5290983 0.0082617 -185.083 < 2e-16 ***
DESTIN_SZPLSZ01 -0.3567934 0.0074298 -48.022 < 2e-16 ***
DESTIN_SZPLSZ02 -1.7114351 0.0134462 -127.280 < 2e-16 ***
DESTIN_SZPLSZ03 -0.3241427 0.0098895 -32.776 < 2e-16 ***
DESTIN_SZPLSZ04 -1.7117196 0.0119003 -143.838 < 2e-16 ***
DESTIN_SZPLSZ05 -0.5086379 0.0120051 -42.368 < 2e-16 ***
DESTIN_SZPNSZ01 0.2026781 0.0068977 29.383 < 2e-16 ***
DESTIN_SZPNSZ02 0.8313754 0.0078544 105.848 < 2e-16 ***
DESTIN_SZPNSZ03 -0.4041254 0.0086586 -46.673 < 2e-16 ***
DESTIN_SZPNSZ04 1.5814539 0.0093641 168.885 < 2e-16 ***
DESTIN_SZPNSZ05 1.1823430 0.0129843 91.059 < 2e-16 ***
DESTIN_SZPRSZ01 -1.1057553 0.0088197 -125.374 < 2e-16 ***
DESTIN_SZPRSZ02 0.0895099 0.0056308 15.897 < 2e-16 ***
DESTIN_SZPRSZ03 0.6921925 0.0043977 157.397 < 2e-16 ***
DESTIN_SZPRSZ04 -0.2848336 0.0084725 -33.619 < 2e-16 ***
DESTIN_SZPRSZ05 0.1744480 0.0053553 32.575 < 2e-16 ***
DESTIN_SZPRSZ06 0.4279206 0.0058735 72.856 < 2e-16 ***
DESTIN_SZPRSZ07 -1.5123108 0.0124303 -121.664 < 2e-16 ***
DESTIN_SZPRSZ08 -0.5650226 0.0068530 -82.449 < 2e-16 ***
DESTIN_SZQTSZ01 -0.5952360 0.0090505 -65.769 < 2e-16 ***
DESTIN_SZQTSZ02 -0.7728170 0.0078910 -97.937 < 2e-16 ***
DESTIN_SZQTSZ03 -0.5066812 0.0073996 -68.474 < 2e-16 ***
DESTIN_SZQTSZ04 -0.6398414 0.0075411 -84.847 < 2e-16 ***
DESTIN_SZQTSZ05 -0.4354527 0.0069345 -62.795 < 2e-16 ***
DESTIN_SZQTSZ06 -0.6597391 0.0071919 -91.733 < 2e-16 ***
DESTIN_SZQTSZ07 -0.9392696 0.0112518 -83.477 < 2e-16 ***
DESTIN_SZQTSZ08 0.4617774 0.0057011 80.998 < 2e-16 ***
DESTIN_SZQTSZ09 -0.3174497 0.0065890 -48.178 < 2e-16 ***
DESTIN_SZQTSZ10 0.1993449 0.0059923 33.267 < 2e-16 ***
DESTIN_SZQTSZ11 0.2551535 0.0061885 41.230 < 2e-16 ***
DESTIN_SZQTSZ12 -0.1662603 0.0086701 -19.176 < 2e-16 ***
DESTIN_SZQTSZ13 0.5500978 0.0063091 87.192 < 2e-16 ***
DESTIN_SZQTSZ14 0.5364435 0.0070157 76.463 < 2e-16 ***
DESTIN_SZQTSZ15 1.3611043 0.0081643 166.715 < 2e-16 ***
DESTIN_SZRCSZ01 -0.1034049 0.0076769 -13.470 < 2e-16 ***
DESTIN_SZRCSZ06 -1.0633902 0.0189846 -56.013 < 2e-16 ***
DESTIN_SZRVSZ01 -1.5486221 0.0165272 -93.701 < 2e-16 ***
DESTIN_SZRVSZ02 -2.4092611 0.0326906 -73.699 < 2e-16 ***
DESTIN_SZRVSZ03 -1.5172079 0.0139258 -108.950 < 2e-16 ***
DESTIN_SZRVSZ04 -1.1663615 0.0157430 -74.088 < 2e-16 ***
DESTIN_SZRVSZ05 -2.2404292 0.0281339 -79.634 < 2e-16 ***
DESTIN_SZSBSZ01 -1.3783780 0.0096022 -143.549 < 2e-16 ***
DESTIN_SZSBSZ02 -1.4445213 0.0081630 -176.959 < 2e-16 ***
DESTIN_SZSBSZ03 0.5149906 0.0051663 99.683 < 2e-16 ***
DESTIN_SZSBSZ04 0.2389086 0.0060765 39.317 < 2e-16 ***
DESTIN_SZSBSZ05 -1.2737442 0.0082818 -153.801 < 2e-16 ***
DESTIN_SZSBSZ06 -1.8683520 0.0227277 -82.206 < 2e-16 ***
DESTIN_SZSBSZ07 -0.5993154 0.0184895 -32.414 < 2e-16 ***
DESTIN_SZSBSZ08 0.8156302 0.0059840 136.302 < 2e-16 ***
DESTIN_SZSBSZ09 0.0900611 0.0057054 15.785 < 2e-16 ***
DESTIN_SZSESZ02 -0.6397704 0.0052491 -121.882 < 2e-16 ***
DESTIN_SZSESZ03 0.1714103 0.0042357 40.468 < 2e-16 ***
DESTIN_SZSESZ04 -1.0596175 0.0059865 -177.002 < 2e-16 ***
DESTIN_SZSESZ05 -0.8071891 0.0051229 -157.566 < 2e-16 ***
DESTIN_SZSESZ06 -0.5580934 0.0066216 -84.284 < 2e-16 ***
DESTIN_SZSESZ07 -3.1448863 0.0227788 -138.062 < 2e-16 ***
DESTIN_SZSGSZ01 -0.1795225 0.0060127 -29.857 < 2e-16 ***
DESTIN_SZSGSZ02 -0.2986570 0.0053561 -55.760 < 2e-16 ***
DESTIN_SZSGSZ03 -0.4074671 0.0050609 -80.513 < 2e-16 ***
DESTIN_SZSGSZ04 -0.1505164 0.0050931 -29.553 < 2e-16 ***
DESTIN_SZSGSZ05 -1.9908372 0.0101448 -196.242 < 2e-16 ***
DESTIN_SZSGSZ06 0.6715268 0.0041161 163.148 < 2e-16 ***
DESTIN_SZSGSZ07 -0.4494757 0.0055319 -81.252 < 2e-16 ***
DESTIN_SZSISZ01 -0.5517983 0.0261860 -21.072 < 2e-16 ***
DESTIN_SZSKSZ01 -0.4749154 0.0079257 -59.921 < 2e-16 ***
DESTIN_SZSKSZ02 0.9400302 0.0057218 164.290 < 2e-16 ***
DESTIN_SZSKSZ03 -0.2800377 0.0066081 -42.378 < 2e-16 ***
DESTIN_SZSKSZ04 -1.2570212 0.0145351 -86.482 < 2e-16 ***
DESTIN_SZSKSZ05 -0.2600474 0.0112800 -23.054 < 2e-16 ***
DESTIN_SZSLSZ01 -0.7775604 0.0085818 -90.606 < 2e-16 ***
DESTIN_SZSLSZ04 -0.8586515 0.0073142 -117.396 < 2e-16 ***
DESTIN_SZSRSZ01 -1.1370887 0.0142148 -79.993 < 2e-16 ***
DESTIN_SZTHSZ01 -4.3259988 0.0368554 -117.378 < 2e-16 ***
DESTIN_SZTHSZ03 -2.6632914 0.0252720 -105.385 < 2e-16 ***
DESTIN_SZTHSZ04 -3.1000906 0.0216372 -143.276 < 2e-16 ***
DESTIN_SZTHSZ06 -2.5952642 0.0156340 -166.001 < 2e-16 ***
DESTIN_SZTMSZ01 -0.2092828 0.0059257 -35.318 < 2e-16 ***
DESTIN_SZTMSZ02 1.8238139 0.0039155 465.798 < 2e-16 ***
DESTIN_SZTMSZ03 0.8518259 0.0043636 195.210 < 2e-16 ***
DESTIN_SZTMSZ04 1.0222812 0.0043466 235.191 < 2e-16 ***
DESTIN_SZTMSZ05 0.6323777 0.0060058 105.294 < 2e-16 ***
DESTIN_SZTNSZ01 -0.3336078 0.0074388 -44.847 < 2e-16 ***
DESTIN_SZTNSZ02 -1.0820469 0.0101689 -106.408 < 2e-16 ***
DESTIN_SZTNSZ03 -1.4186505 0.0119906 -118.313 < 2e-16 ***
DESTIN_SZTNSZ04 -0.3058199 0.0074743 -40.916 < 2e-16 ***
DESTIN_SZTPSZ01 -0.4872299 0.0061571 -79.133 < 2e-16 ***
DESTIN_SZTPSZ02 0.7158441 0.0041312 173.278 < 2e-16 ***
DESTIN_SZTPSZ03 -0.4314229 0.0059917 -72.004 < 2e-16 ***
DESTIN_SZTPSZ04 -1.5898245 0.0076083 -208.959 < 2e-16 ***
DESTIN_SZTPSZ05 -1.0445550 0.0062363 -167.497 < 2e-16 ***
DESTIN_SZTPSZ06 -0.4319582 0.0070100 -61.621 < 2e-16 ***
DESTIN_SZTPSZ07 -2.1602303 0.0120352 -179.493 < 2e-16 ***
DESTIN_SZTPSZ08 -1.1920493 0.0093083 -128.063 < 2e-16 ***
DESTIN_SZTPSZ09 -0.2022481 0.0071137 -28.431 < 2e-16 ***
DESTIN_SZTPSZ10 -1.2464793 0.0090124 -138.308 < 2e-16 ***
DESTIN_SZTPSZ11 -0.0808445 0.0056019 -14.432 < 2e-16 ***
DESTIN_SZTPSZ12 -0.6784376 0.0066340 -102.267 < 2e-16 ***
DESTIN_SZTSSZ01 -1.5845062 0.0222086 -71.346 < 2e-16 ***
DESTIN_SZTSSZ02 -0.1886010 0.0146338 -12.888 < 2e-16 ***
DESTIN_SZTSSZ03 0.6525526 0.0092450 70.585 < 2e-16 ***
DESTIN_SZTSSZ04 0.5285464 0.0100182 52.759 < 2e-16 ***
DESTIN_SZTSSZ05 1.4670106 0.0104357 140.577 < 2e-16 ***
DESTIN_SZTSSZ06 2.5043588 0.0167444 149.564 < 2e-16 ***
DESTIN_SZWCSZ01 1.9787931 0.0054306 364.375 < 2e-16 ***
DESTIN_SZWCSZ02 -2.2593108 0.0127916 -176.624 < 2e-16 ***
DESTIN_SZWCSZ03 -3.1897655 0.0326927 -97.568 < 2e-16 ***
DESTIN_SZWDSZ01 1.0476108 0.0044629 234.738 < 2e-16 ***
DESTIN_SZWDSZ02 -1.3176990 0.0065894 -199.973 < 2e-16 ***
DESTIN_SZWDSZ03 0.3432057 0.0052496 65.377 < 2e-16 ***
DESTIN_SZWDSZ04 -0.7895927 0.0073392 -107.586 < 2e-16 ***
DESTIN_SZWDSZ05 -0.8751665 0.0072946 -119.975 < 2e-16 ***
DESTIN_SZWDSZ06 -0.2106221 0.0053027 -39.720 < 2e-16 ***
DESTIN_SZWDSZ07 -1.6050834 0.0071754 -223.692 < 2e-16 ***
DESTIN_SZWDSZ08 -0.5124717 0.0069223 -74.032 < 2e-16 ***
DESTIN_SZWDSZ09 0.3813542 0.0054697 69.721 < 2e-16 ***
DESTIN_SZYSSZ01 0.0853753 0.0046572 18.332 < 2e-16 ***
DESTIN_SZYSSZ02 -0.3227172 0.0057351 -56.271 < 2e-16 ***
DESTIN_SZYSSZ03 -0.4151283 0.0066299 -62.615 < 2e-16 ***
DESTIN_SZYSSZ04 -0.4637327 0.0058206 -79.671 < 2e-16 ***
DESTIN_SZYSSZ05 -1.5888242 0.0111001 -143.136 < 2e-16 ***
DESTIN_SZYSSZ06 -1.4606209 0.0107759 -135.545 < 2e-16 ***
DESTIN_SZYSSZ07 -0.7839065 0.0144357 -54.304 < 2e-16 ***
DESTIN_SZYSSZ08 0.6265412 0.0045504 137.691 < 2e-16 ***
DESTIN_SZYSSZ09 0.1520067 0.0048092 31.607 < 2e-16 ***
log(dist) -1.8468315 0.0004608 -4008.033 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 47094011 on 14470 degrees of freedom
Residual deviance: 10420261 on 13912 degrees of freedom
AIC: 10510518
Number of Fisher Scoring iterations: 7Again, let’s check the R-square values of doubly constrained SIM model this time.
CalcRSquared(dbcSIM$data$TRIPS, dbcSIM$fitted.values)[1] 0.7001882Notice that there is a relatively greater improvement in the R-sqauared value than destination constrained SIM.
9.7 Model Comparison
Another useful model performance measure for continuous dependent variable is Root Mean Squared Error. In this sub-section, you will learn how to use compare_performance() of performance package.
First of all, let us create a list called model_list by using the code chunk below.
model_list <- list(unconstrained=uncSIM,
originConstrained=orcSIM,
destinationConstrained=decSIM,
doublyConstrained=dbcSIM)Next, we will compute the RMSE of all the models in model_list file by using the code chunk below.
compare_performance(model_list,
metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
-----------------------------------------
unconstrained | glm | 3178.342
originConstrained | glm | 2697.969
destinationConstrained | glm | 2434.018
doublyConstrained | glm | 1906.694The print above reveals that doubly constrained SIM is the best model among all the four SIMs because it has the smallest RMSE value of 1906.694.
9.8 Visualising fitted values
Firstly we will extract the fitted values from each model by using the code chunk below.
df_unc <- as.data.frame(uncSIM$fitted.values) %>%
round(digits = 0)Next, we will join the values to SIM_data data frame.
SIM_data <- SIM_data %>%
cbind(df_unc) %>%
rename(uncTRIPS = "uncSIM$fitted.values")We repeat the same step by for Origin Constrained SIM (i.e. orcSIM)
df_orc <- as.data.frame(orcSIM$fitted.values) %>%
round(digits = 0)SIM_data <- SIM_data %>%
cbind(df_orc) %>%
rename(orcTRIPS = "orcSIM$fitted.values")We repeat the same step by for Destination Constrained SIM (i.e. decSIM)
df_dec <- as.data.frame(decSIM$fitted.values) %>%
round(digits = 0)SIM_data <- SIM_data %>%
cbind(df_dec) %>%
rename(decTRIPS = "decSIM$fitted.values")We repeat the same step by for Doubly Constrained SIM (i.e. dbcSIM)
df_dbc <- as.data.frame(dbcSIM$fitted.values) %>%
round(digits = 0)SIM_data <- SIM_data %>%
cbind(df_dbc) %>%
rename(dbcTRIPS = "dbcSIM$fitted.values")Next, we will create plots for each model.
unc_p <- ggplot(data = SIM_data,
aes(x = uncTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
orc_p <- ggplot(data = SIM_data,
aes(x = orcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
dec_p <- ggplot(data = SIM_data,
aes(x = decTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)
dbc_p <- ggplot(data = SIM_data,
aes(x = dbcTRIPS,
y = TRIPS)) +
geom_point() +
geom_smooth(method = lm)Now, we will put all the graphs into a single visual for better comparison by using the code chunk below.
ggarrange(unc_p, orc_p, dec_p, dbc_p,
ncol = 2,
nrow = 2)`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'